How do I develop mobile applications for Bitcoin? I would like to develop a mobile Bitcoin application for the Android and iPhone platforms.  What libraries and resources can I use?
Currently there are only a few mobile apps that use the bitcoin protocol itself. Most communicate with a bitcoin client on a remote machine using the JSON API.

Those few that do, rely on BitcoinJ which is a "selfish" implementation of bitcoin that runs in Java (handily the native language for Android apps). It's got a few key modifications that bring its overhead low enough to run on embedded devices, most notably it does not download all blocks in the block-chain, only those blocks which relate to addresses in its own wallet (hence "selfish" client).

Either method works, and either is as valid a starting point as the other, given the current state of bitcoin's mobile development.