The UK is run by a minority government right now, and will remain run by a minority government until the next election. What happens in a minority government is rather simple: a party or group of parties governs without a governing majority and is dependent on the lack of a no-confidence vote to retain power. So in this situation that the UK is currently in, should the DUP pull out of the confidence-and-supply agreement they are currently in with the Tories and vote no confidence in them, those votes combined with the other votes of the chamber would be enough to force a general election.
Similarly, should no party gain a governing majority after the 2022 elections and no coalition be formed, parties would try and form minority governments that wouldn't lose a confidence motion. The incumbent prime minister (which if Theresa May is to be believed won't be Theresa May) and their party gets first dibs, but back in 2010 while coalitions were being negotiated, then-PM Gordon Brown refused those dibs since the Tories had more seats, giving David Cameron the first shot at a confidence motion. (Cameron then negotiated with Nick Clegg's Lib Dems to form a coalition government, of course.) In any case, such a government is always vulnerable to a snap election as a result of a lost confidence motion.