In the premier episode, Voyager and time traveller Phineas Bogg accidentally materializes outside the bedroom of a 12-year old orphan, Jeffrey Jones, in 1982. Jeff tries to stop his dog from running off with Bogg's chronological guidebook, and falls out a window. Bogg has to save him by jumping after Jeff and then activating his time travel device (an ""Omni""). Without the guidebook, the two end up in Egypt (and a meeting with an infant Moses). They then travel to World War I France and discover that the airplane has never been invented. Bogg flunked out of his history classes at the Voyager academy, but fortunately Jeff is a history whiz. They travel back to Dayton, Ohio and help the Wright Brothers invent the first airplane. Successful, they travel back to WWI to make sure history is back on track. It is, but they end up in an aerial battle with the Red Baron. With some help from Eddie Rickenbacker, they emerge triumphant. The Omni is not entirely accurate, which means Bogg can't retu

Arriving in Italy in 73 B.C., the pair discover that Spartacus is being sent to die in the arena in Rome, altering history and preventing him for leading the slave revolt in Capra. They are bought as slaves but when their escape attempt fails, they have to Omni out. That puts them in Hannibal Missouri in the 19th century, where they encountered Harriet Tubman. She is still a slave, having never formed the Underground Railroad. While Jeff and a young Sam Clemens try to free her, Bogg manages to ""purchase"" her in a poker game. With history back on track, it's back to Rome, where Bogg ends up fighting Spartacus in the arena. Jeff and his newfound friend Calpernia manage to steal a chariot belonging to her father Cicero, break out Bogg and Spartacus, and get history back on track.

Jeff and Bogg arrive in the Cuban revolution, to find history changed because Teddy Roosevelt never led the charge up San Juan history. He was killed by Billy the Kid in 1889. The Voyagers head back to that time, stopping briefly to help Ben Franklin get his kite in the air. Once back in the Old West, the two infiltrate Billy's gang and then save Roosevelt's life. Billy turns out to be a coward without his gun, much to Jeff's dismay. Travelling back to Cuba to make sure history is on track, they meet up with Roosevelt and help the Cuban rebels, setting history right.

Bogg and Jeff land in colonial Massachusetts. Their arrival is witnessed by a local who has them arrested as witches. Benjamin Franklin's mother is also under accusation, and if she dies, history changes. Jeff uses the Omni to prevent him and Bogg from being burned at the stake, but that puts them a couple of centuries forward and right in the middle of a seance being attended by skeptic Harry Houdini. Witnessing the ""supernatural"" with his own eyes, Houdini starts believing in ghosts, further altering history. The Voyagers Omni out, but return when Jeff determines they must convince Houdini they aren't ghosts. He and Bogg end up saving Houdini from being rescued alive, and put that part of history back on track. They then return to Massachusetts with one of Houdini's mirror illusions. Using it, they show that there are no such thing as ghosts and witches: only mechanical trickery. That ends the witch trials, and history is restored.

The Voyagers are separated: Bogg is with Lawrence of Arabia, while Jeff is stranded in the 1800's with Thomas Alva Edison. When Jeffrey awakes after a rough landing, he learns that Edison has dismantled the Omni and not invented the light bulb. A piece of thread is the answer to the incandescent light but Edison can't figure out the Omni. He rebuilds the strange device and Jeff returns to Arabia, unknowingly saving Bogg and Lawrence as they are being led to their deaths. A chase through the catacombs leads Lawrence, Medina, and the Voyagers to safety and Lawrence is reunited with his people. The Voyagers return to Menlo Park to see the electric light used outdoors for the first time.

The Voyagers inadvertently bring Cleopatra forward in time to prohibition-era New York City, where she encounters gangster Lucky Luciano. In the main plot, Phineas has to convince young baseball player Babe Ruth to abandon his pitching career so that he will eventually become the home run hitter idolized by Jeffrey.

On their way to rescue President Lincoln, who has been kidnapped by Confederate soldiers, the Voyagers are briefly diverted to 1832 London where they encounter young author Charles Dickens.

Jeffrey and Bogg talk the pirate, Jean Lafitte, into leaving the beautiful Bahamas for New Orleans where General Jackson is going to need his help against the Red Coats.

Jeff and Bogg arrive in 1930's New York and meet a retired adventurer/voyager, Isaac Wolfstein. They drop him off on an island to live out the rest of his life, save Albert Einstein, then pop back to Marco Polo's time...but Polo isn't where he's supposed to be. The two try to restore histroy but Jeffrey is caught by soldiers who plan to sell him as a slave. Bogg goes to Wolfstein to get advice, and just manages to save him from a nuclear test on the island. The two men return to save Jeffrey, then head off to lunch with Einstein.

The Voyagers encourage Lindburgh on the eve of his trans-atlantic flight, then help Robin Hood sneak into an archery competition to rescue Maid Marian.

The Voyagers must go back in time to before the American Revolution to make sure that George Washington joins the American rebels rather than the British. Then in 1892 they help early union leader Samuel Gompers, and Jeffrey gets to meet his great grandfather, a lawyer helping the labor cause.

First, the Voyagers help Albert Schweitzer in his efforts to bring medical aid to a dying African tribal chief. Then they arrive in 1887 to help Annie Oakley, who is with Buffalo Bill's circus that is in England to perform for Queen Victoria.

Jeff and Bogg are intercepted en route and land in a dark limbo. The Omni is dead, and they soon find out that they have been brought to a Voyager courtroom, where Bogg is put on trial for breaking the Voyager code of ethics. The prosecutor, Drake, uses Bogg's Omni memory banks to prove that he is guilty, but they discover that Drake tampered with the records and is trying to frame Bogg. Drake escapes, taking Bogg and Jeff with him. They end up in Texas in the 19th century, and the duo have to let Drake escape so that they can save Sam Houston from a firing squad. The two are brought back to the the courtroom, and Jeff is made an official Voyager. However, they depart on Drake's trail, forgetting to pick up a guidebook.

Arriving at Pearl Harbor on 6 December 1941, the Voyagers try to warn General MacArthur about the upcoming Japanese attack. Then then end up in 1860's Utah to help a young Buffalo Bill Cody with the Pony Express mail service.

Phineas and Jeffrey assist a fellow Voyager who is trying to recover the stolen Mona Lisa from a thief aboard the doomed ocean liner Titanic. Then in 1884 France, Jeffrey is bitten by a rabid dog and his only chance of survival is treatment with a new vaccine invented by Louis Pasteur.

In order for the future American Space Program to succeed, the Voyagers must go back to Austria just after the end of World War II and prevent rocket scientist Werner Von Braun from being captured by the Soviets.

Phineas and Jeffrey journey back to 1924 Hollywood to convince Franklin D. Roosevelt to give up on a career as a film director and go into politics instead.

The Omni lands Bogg and Jeff in New Jersey, 1938, where they find Joe Louis ready to quit boxing while preparing for his rematch with Max Schmeling. Bogg becomes his sparring partner to convince him otherwise, but a lucky punch on his part manages to knock out Louis and even further convince him to quit for good. Hostile fight-ring workers dont' take kindly to Bogg, and he and Jeff escape to a 747 in 1970. Jeff ends up piloting the craft when terrorists knock everyone else out with gas. After a safe landing, the duo return to 1938, where they put Louis on a Rocky-style training regimen. Louis ends up beating Schmeling and history is back on track.

The Voyagers appear in 1890 in Texas, and find that Dwight Eisenhower's mother is unable to give birth to him because of the absence of a doctor. They are unable to call for help because the telephone doesn't exist! Travelling to 1875 Boston, they try to find what happened to Alexander Graham Bell. Bogg rescues a young deaf girl, and then they find out that Bell discontinued his experiments due to a lack of funds. Jeff remembers that Bell got his money from his fiancee, who turns out to be the deaf girl Bogg rescued. They must unite the couple, but Bogg falls in love with the girl in the process. Eventually he leaves her so that history can stay on track. After checking a few months down the road to make sure Bell does indeed invent the telephone, they return to 1890, where things work out and Dwight Eisenhower is born, setting history back on track.

Bogg and Jeff land in 1880 London and save famous world-traveller Nellie Bly from Jack the Ripper. The three of them meet with Sir Arthur Conan Doyle, who is suffering from writers' block. Besides making sure Doyle write his Holmes novels and Bly goes on her famous world trip, they discover that Bogg's nemesis, the evil renegade Voyager Drake (from The Trial of Phineas Bogg) is the one who tries to kill Bly as Jack the Ripper.