Set in the then-future year of 1983, the series tells the tale of the crew and passengers of a sub-orbital transport spaceship called the Spindrift. In the pilot episode, the Spindrift is en route from Los Angeles to London via the ultra-fast route of a parabolic trajectory. Just beyond Earth's boundary with space, the Spindrift encounters a strange space storm and is transported to a mysterious planet where everything is twelve times larger than its counterpart on Earth. The Spindrift crew calls the inhabitants "the giants". Given relative proportions shown on the show, the giants are about 72 feet tall. Everything on their planet is built to their scale — buildings, cars, animals, etc. The Spindrift crashes on this planet and becomes inoperable.

These giants are humanoid in form, but their society is a dictatorship of which not too many details are given, and that employs no symbols. The giant government has offered a reward for the capture of the tiny Earth people, presumably because of the Earth people's superior technology. Episodes often have the plot of giants capturing one of the passengers or crew, with the rest having to rescue the captive. The Earth people avoid capture most of the time because their spaceship is hidden in a forest outside the city.

Very little is known about the home planet of the Giants. That is partially because the Spindrift crew very seldom leaves the "City of the Giants" where their spaceship crashed in the pilot. Only two other societies are ever seen: they are "The Land of the Lost" and "Secret City of Limbo" both of which are glimpsed only briefly. Both are descriptive phrases rather than names. No name is ever given for either of these societies.

No name has ever even been established for the mysterious planet, but the inhabitants seem to know of Earth, Venus and Mars, referring to them by name in one episode. (The first mention of Earth by the giants was in the second episode, and was matter of factly mentioned.) This may be because of prior crashes of ships from Earth. Exactly where this planet is located is also never made clear. However it can be supposed that it is a natural part of the Earth's solar system, but is, by some quirk of nature/parallel universe, unknown to Earth, perhaps the natural warp that transits ships from Earth also prevents the passage of light and perhaps even gravity perturbations. In the episode, "On a Clear Night You Can See Earth", the character Captain Steve Burton (Gary Conway) claims to have seen Earth through a set of infrared goggles invented by the giants, implying that the two worlds are indeed different but near enough to each other to be able to see one from the other. Whether or not he is telling the truth is unclear.

The only established method by which Earth people may reach the planet is some sort of high-altitude spacecraft, passing through what one giant calls a "dimension lock" which seems to act more as a space warp or wormhole. The first (and only) mention of the phrase "dimension lock," by a giant in the second episode of the first season ("Ghost Town"). The giant refers to the space warp as "our dimension lock," as if it were built or at least known by the inhabitants of the giant planet. The Spindrift crew just calls it a space warp. The term wormhole is never used. It is not entirely clear what the term dimension lock means. It is possible that the "dimension lock" is a peculiarity of the Giants' planet that keeps it from causing gravity perturbations that would betray its existence such as altering the trajectories of planets, asteroids, comets and Earth space probes.

Although several episodes show that at least six other flights have landed on the planet, no episode shows that anyone ever successfully returned to Earth. The first mention of other visitors from Earth was in episode 2 ("Ghost Town"), where another ship was described as crashing long ago without any survivors. In episode 4 ("Underground") another Earth ship is described as crashing three years prior with no survivors.

Several episodes show crews surviving the initial crash, only to be killed later. The episode "Brainwash" has a crew of little people surviving long enough to build a radio station that can communicate with Earth. They are killed shortly thereafter. The episodes "Golden Cage" and "The Lost Ones" show survivors of other crashes, where only certain crew members have survived. Only the Spindrift crew seems to have survived long term, with its party intact. The impression given is that Earth people do not do well for long in giant captivity.

One country or continent or hemisphere is wholly dominated by an authoritarian government which, however, tolerates the existence of entrepreneurs and businessmen. Giant society does not seem very militarized nor is day-to-day life restricted with curfews and other regulations; it simply does not tolerate any effort to effect political change. In the episode "Doomsday" it is mentioned that there are many nations on this giant planet. Exactly what the political situation is on other continents is not known, although at least one overseas land ("The Land of the Lost") has a despotic ruler. The Air Traffic Control will tell those who venture far out to sea that they should turn back, that nothing beyond that sea has been explored nor is their current contact; whether this is an official government line or the truth is not known. It should be noted that the Air Traffic Controller has behind him what appears to be a map of the giant planet.

In spite of the authoritarian government, there are several dissident movements at work that either help other dissenters (such as the Earth people) or are actively working to unseat the government. Whether or not these dissidents are any better than the government is not known. In later episodes the Earth people end up fighting with these dissidents. They do this to stop efforts to disrupt giant society. The government has established the SID, Special Investigations Department, to deal with assorted dissidents, but it also has taken the lead in dealing with the Earth people.

The technology largely resembles 1950s and 1960s Earth, slightly more advanced in some respects (e.g. cloning, radio controlled toys, small nuclear reactors) and slightly behind in others (does not have microelectronics, hearing aids, or manned space flight). Culturally, the society resembles the United States. The Earth people find themselves able to cope at a cultural level, dealing with movie studios, musicians, hobos, nuclear families, orphanages, folklore, jealousies and rivalries, law-breakers and patriots, criminals and honest people, poor and rich, sympathetic and hostile. Their efforts to get around are facilitated by the ubiquity of large drains directly from interior rooms to the pavement level at an outside wall of most buildings. The fact that English is the local language no doubt adds to these conveniences. (In the first few episodes a made-up language is used for signage but this is quickly dropped. English is spoken throughout).

The Earth people's objectives are: (1) survival, by obtaining food and by avoiding capture by the native people or menace from small animals like cats and dogs; (2) repair of their spacecraft so they may take off and attempt a return to Earth. They largely manage survival with the help of their ingenuity, their small size (enabling them to sneak around and hide), the occasional giant sympathizer, and, of course, their technology, which (per dialogue spoken in one of the episodes) is about fifty years ahead of the giants' technology.

They do not achieve the second objective, however, since the primary systems of their craft, the Spindrift, are heavily damaged, and they may have had to use precious resources in order to safeguard themselves from capture. The secondary systems are insufficient to allow take-off and the sub-orbital flight required. They are unable to successfully integrate the native technology as it is bulky and less advanced; in one episode, an experimental nuclear reactor provided by an engineering student produces dangerous side effects and is prone to overload. They also cannot trust the giants who might be able to offer the Earth people a ride home in exchange for technical assistance.

They are aided in the first goal, and at least somewhat hindered in the second, by the leadership of Captain Steve Burton. He behaves as leader, protector to the passengers and crew and his leadership has rescued them from a number of difficulties. However, Captain Burton also functions as a guardian of the gate who tries to keep the giants from ever reaching Earth. In the episode "Brainwash", giant police officer Ashim (Warren Stevens) says "Maybe we can find the home planet of these little people. It may be a very tiny planet, but rich beyond our dreams." It is not entirely clear what that means. Nor is it entirely clear what the giants would do if they ever reached Earth. In several episodes Captain Burton puts keeping the giants away from Earth above the need to get his people home. At the end of those episodes he destroys devices that would get the Spindrift back to Earth but would probably also enable the giants to journey there as well.

The Crash

September 22, 1968

Ghost Town

September 29, 1968

Framed

October 6, 1968

Underground

October 20, 1968

Terror-Go-Round

November 3, 1968

The Flight Plan

November 10, 1968

Manhunt

November 17, 1968

The Trap

November 24, 1968

The Creed

December 1, 1968

Double-Cross

December 8, 1968

The Weird World

December 22, 1968

The Golden Cage

December 29, 1968

The Lost Ones

January 5, 1969

Brainwash

January 12, 1969

The Bounty Hunter

January 19, 1969

On a Clear Night You Can See Earth

January 26, 1969

Deadly Lodestone

February 2, 1969

Night of Thrombeldinbar

February 16, 1969

Seven Little Indians

February 23, 1969

Target: Earth

March 2, 1969

Genius at Work

March 9, 1969

Return of Inidu

March 16, 1969

Rescue

March 23, 1969

Sabotage

March 30, 1969

Shell Game

April 13, 1969

The Chase

April 20, 1969

The Mechanical Man

September 21, 1969

Six Hours to Live

September 28, 1969

The Inside Rail

October 5, 1969

Deadly Pawn

October 12, 1969

The Unsuspected

October 19, 1969

Giants and All That Jazz

October 26, 1969

Collector's Item

November 2, 1969

Every Dog Needs a Boy

November 9, 1969

Chamber of Fear

November 16, 1969

The Clones

November 23, 1969

Comeback

November 30, 1969

A Place Called Earth

December 7, 1969

Land of the Lost

December 14, 1969

Home Sweet Home

December 21, 1969

Our Man O'Reilly

December 28, 1969

Nightmare

January 4, 1970

Pay the Piper

January 11, 1970

The Secret City of Limbo

January 18, 1970

Panic

January 25, 1970

The Deadly Dart

February 1, 1970

Doomsday

February 15, 1970

A Small War

February 22, 1970

The Marionettes

March 1, 1970

Wild Journey

March 8, 1970

Graveyard of Fools

March 22, 1970