Carbon dating suggests that most of the underground work on the Island dates from the early 17th century. Other finds (coconut fiber) indicate earlier dates, suggesting at least two phases of construction and occupation. These dates and the complexity of the work rule out most of the theories - pirates (too complex and no easy recovery option), the British army (too late), the French (too late), Arcadians (too late), the Incas (too preposterous)......
There are some great books on the topic. I recently read The Secret Treasure of Oak Island by D'arcy O'Connor and the recently published Curse of Oak Island by Randall Sullivan, which I highly recommend. Sullivan comes to the same conclusions as me and favors the Francis Bacon line of thinking. This is probably the wildest and most complex theory out there as it incorporates the Knights Templar, Rosicrucians, Freemasons, Shakespeare, the Arc of the Covenant and enough esoterica to drive you insane.
They continuously touch on the topic on the show but for now they remain transfixed by the money pit. For a number of reasons the swamp has not been explored further which is unfortunate because, like many others, I believe this is where the answers will be found. Norwegian researcher Petter Amundsen has been the leading proponent of this theory but he fell out of favor with the current Oak Island team when he sided with the Canadian authorities and pushed for an archeologist to be involved in the search operations (hence Laird Niven).
Check out Amundsens documentaries Timeline - Shakespeare part 1 they are fascinating