Some cryptocurrencies can be traded in a trustless manner, also known as atomic cross-chain traded. This means that when the trade is done, either the entire trade is done, or none of it is (otherwise, one party could choose not to send their coins).
Can this be done between Bitcoin and Monero. Monero doesn't have scripting support, so the above link's protocol wouldn't work.
One application for this is recovering stolen Bitcoins. If your Bitcoins are stolen, you can buy them back at a discount from the attacker. Since you don't trust each other, or even trust a common arbitrator, it needs to be a trustless trade. You won't recover all your wealth (since you had to give up some of your Monero, which you may have had to buy), but since its at a discount, you'll have recovered some of it. (The thief is likely to accept this, since otherwise he would need to go through the process of laundering the bitcoins.)