What energy are submarines powered by?

Up until the 1954 launch of the USS Nautilus(SSN-571), the world's first nuclear powered submarine, all submarines of the 20th Century were Diesel-Electric powered, meaning they ran on their diesel engines on the surface, and battery-powered electric motors when they were submerged. DE's are still in operation today, with submergence longevity far exceeding that of previous counterparts.

For blue-water navies, nuclear power is the main power generation of choice, due to its time between refueling (years rather than weeks), tactical advantages (increased speeds and weapons/tactical capability), and crew habitation (continuous atmosphere regeneration, water availability, etc.). Most countries that either don't or cannot afford a strategic submarine element in their Navies maintain Diesel-Electric submarines on a small scale. The current battery technology has risen to the level where DE submarines can go for almost a month before the need to recharge.