An elderly artist thinks he has become too stale and is past his prime. His friend (and agent) persuades him to go to an offshore island to try once more. On the island he re-discovers his muse in the form of a young girl.

In Dublin circa 1911, John Cassidy (Rod Taylor), an impoverished idealist, whose ambitions are restricted by the demands of looking after his family, journeys through the social injustices of Dublin life, involving himself with the rowdy tramway-men strike, dawdling with prostitute Daisy Battles (Julie Christie), and seeking a better life. He falls in love with bookshop assistant Nora (Dame Maggie Smith) who encourages him toward a life of writing. Finding success at the Abbey Theatre, his unorthodox views estrange him from family, friends, and his own past.

Dutch painter Jan-Van Rooyer hurries to keep a rendezvous with Jacqueline Cousteau, an elegant, sophisticated Frenchwoman, slightly his elder, whose relationship with him had turned from art student into one of love trysts. He arrives and is confronted by Detective Police Inspector Morgan who accuses him of having murdered Jacqueline. Morgan listens sceptically to the dazed denials of Van Rooyer as he tells the story of his relationship with the murdered woman. Morgan, after hearing the story, realizes that the mystery has deepened, and it becomes more complicated when the Assistant Commissioner, Sir Brian Lewis, explains that Jacqueline was not married but was being kept by Sir Howard Fenton, a high-ranking diplomat whose names must be kept out of the case.

A wily old codger matches wits with the King of the Leprechauns and helps play matchmaker for his daughter and the strapping lad who has replaced him as caretaker.

After the mysterious crash of a millionaire's private plane, scientists secretly harvest the dying man's brain and keep it alive in a laboratory in order to communicate via telepathy.

Marine atomic tests cause changes in the ocean's ecosystem resulting in dangerous blobs of radiation and the resurrection of a dormant dinosaur which threatens London.

Three vignettes of old Irish country life, based on a series of short stories. In "The Majesty of the Law," a police officer must arrest an old-fashioned, traditional fellow for assault. The man's principles have the policeman and the whole village, including the man he slugged, sympathizing with him. "One Minute's Wait" is about a little train station and glimpses into the lives of the passengers, with a series of comic setups. The third piece, "1921," is about a condemned Irish nationalist and his daring escape.