Range anxiety became a major issue for navies during the transition from sail to steam power, because while ships could be victualed for six months or so and wind was free, early steam ships had horribly inefficient engines and burned coal at a furious rate. I wrote a couple of answers about the sail-to-steam transition here:

https://www.reddit.com/r/AskHistorians/comments/2jso46/how_did_the_transition_from_wooden_ships_to/

and here:

https://www.reddit.com/r/AskHistorians/comments/2gv83n/what_sort_of_jobs_did_the_crew_do_on_an/

Early steam warships generally had masts to complement their steam powerplants, or in some cases were sailing warships converted to steam power, so that they could use both means of propulsion when necessary. The problem that navies faced was that both types of propulsion made the other inefficient; the drag of the propellors underwater hampered sailing as much as the drag of the top-hamper decreased the efficiency of the steam engines.

In response, navies set up coaling stations at various spots around the globe, and (at least in Britain) negotiated agreements with merchant shipping lines to be able to seize coal from their ships in the event of war or an emergency. As engine efficiency improved, eventually it became quite apparent that hauling masts and sails around didn't make a lot of sense (in 1875, an RN captain ran numbers to prove this), and ships eventually lost the masts except for signaling and antenna purposes.

The British navy, interestingly, faced a related range anxiety question in the run-up to World War I. There had been arguments over using coal or fuel oil for propulsion from the very early days of steam engines; coal had to be moved around manually, required the work of skilled stokers to burn efficiently, and has a lower thermal efficiency than oil. Oil, on the other hand, can be pumped around the ship, can be fed into boilers automatically, and requires much less manual labor aboard ship. It's also got a higher thermal efficiency than coal, burns much cleaner than coal, and doesn't coat everything on board with coal dust. (Here's a picture of the Grand Fleet heading to the battle of Jutland; most ships were still coal-fired so you get an idea of the smoke/haze/visibility problem.)

Now, the problem is that coal is abundant in the British isles (Wales is made of the stuff), but there were no domestic sources of oil in 1901, when Jackie Fisher started agitating for oil-fired ships. (Offshore platforms came much later.) So by adopting coal oil-fired capital ships, which the British did with the Queen Elizabeth claps in 1912, they tied themselves inextricably to foreign sources of oil for strategic reasons.