At a meeting of the Astronomic Club, its president, Professor Barbenfouillis, proposes a trip to the Moon. After addressing some dissent, five other brave astronomers—Nostradamus, Alcofrisbas, Omega, Micromegas, and Parafaragaramus—agree to the plan. They build a space capsule in the shape of a bullet, and a huge cannon to shoot it into space. The astronomers embark and their capsule is fired from the cannon with the help of "marines", most of whom are played by a bevy of young women in sailors' outfits. The Man in the Moon watches the capsule as it approaches, and it hits him in the eye.
In 1965, a series of mysterious and devastating incidents are happening on Earth. These incidents range from a railroad bridge levitated off the ground causing a train wreck in Japan; an ocean liner lifted out of the Panama Canal by a waterspout, destroying it; severe flooding in Venice, Italy; and the destruction of the J-SS3 space station.
Phineas T. Barnum (Burl Ives) and friends finance the first flight to the moon but find the task a little above them. They attempt to blast their rocket into orbit from a massive gun barrel built into the side of a Welsh mountain, but money troubles, spies and saboteurs ensure that the plan is doomed before it starts...
In the British city of "Everytown", businessman John Cabal (Raymond Massey) cannot enjoy Christmas Day, 1940, with the news everywhere of possible war. His guest, Harding (Maurice Braddell), shares his worries, while his other friend, the over-optimistic Pippa Passworthy (Edward Chapman), believes it will not come to pass, but if it does, it will accelerate technological progress. An aerial bombing raid on the city that night results in general mobilisation and then global war.
In the year 1946, the Soviet space program is undergoing turmoil. Professor Sedikh, who is planning to lead the first manned exploration to the moon, is denounced by his rival Professor Karin as being too old and too mentally unstable for the mission. Professor Sedikh, aided by his assistant Marina and a youth named Andryusha, disregard Prof. Karin’s authority and make a successful landing on the moon. Although a few problems occur at the moon, including the discovery of a damaged oxygen tank and Professor Sedikh’s becoming trapped under a fallen boulder, the expedition is a success and the cosmonauts return to Moscow.
Set in a future 1970, the United States is considering building bases on the Moon. Colonel Briteis (Donna Martell), Major Bill Moore (Ross Ford), and Doctor Wernher (Larry Johns) are sent to orbit the Moon to survey landing sites for future lunar missions. However, Dr. Wernher is an impostor whose mission is to destroy the US's Earth-orbiting space station, which he plans to do by colliding the rocket with the station on the way back from the Moon.
Astronaut Capt. Richmond Talbot inadvertently volunteers to make the first manned flight around the moon. He is ordered to keep the upcoming moon flight a secret, even from his family. Due to the classified nature of the mission, he is placed under the watchful eye of several national security agencies.
The spaceship AAB Gamma is dispatched from Japan to travel to Mars to investigate reports of UFOs in the area. When the Gamma nears the red planet, it comes across a mysterious alien vessel that sprays the ship with spores. Samples are taken back to earth where one of them begins to develop.
The radio telescope at Parkes (Parkes Observatory), New South Wales, Australia, was used by NASA throughout the Apollo program to receive signals in the Southern Hemisphere, along with the NASA Honeysuckle Creek Tracking Station near Canberra.
Financial disaster looms for Grand Fenwick when the current vintage of its only export, wine, starts exploding in would-be consumers' faces. Prime Minister Mountjoy (Ron Moody) decides to ask the United States for a loan, ostensibly to fund its entry in the race to the Moon, but actually to save the duchy (and install modern plumbing so he can have a hot bath). The devious politician knows that the Americans will not believe him, but will consider the half million dollars he is asking for to be cheap propaganda supporting their hollow call for international co-operation in space. He is delighted when they send him double the amount as an outright gift. The Soviets, not wishing to be one-upped by their Cold War rivals, deliver an obsolete rocket. Mountjoy asks resident scientist Professor Kokintz (David Kosoff) to arrange a small explosion during the "launch" of their lunar rocket to make it look like they have actually spent the money as intended.
The film opens at an 18th-century ball, where Baron Hieronymus von Münchhausen is propositioned by a young woman who is engaged to another man. He graciously rejects her advance, and as she leaves, she asks him to turn on the light. The camera follows his hand to a modern light switch, and the young woman drives off in an automobile. The next day, the Baron, out of his costume and in modern dress, regales two of his guests with stories of the famous Baron Münchhausen, to whom his guests think he is distantly related.
Brick Bradford is assigned by the government to aid Doctor Gregor Tymak, scientist and inventor who is working on an "Interceptor Ray" that can destroy incoming rockets. Unfortunately, it can also be used as a death ray, bringing it to the attention of foreign spy agent Laydron. Tymak uses his door into the fifth dimension to escape criminals and it takes him to the far side of the Moon (which luckily has air and is a rocky terrain without craters). There he is captured and sentenced to die by freezing to absolute zero by the Queen Khana, despot of the Moon, because they do not believe he has come from the Earth.
An expedition to the moon encounters a race of "Cat-Women", the last eight survivors of a 2-million-year-old civilization, deep within a cave where they have managed to maintain the remnants of a breathable atmosphere that once covered the Moon. The remaining air will soon be gone, and they must escape if they are to survive. They plan to steal the expedition's spaceship and migrate to Earth.