Desktop-based wallets are all very well, but they aren't very useful if you are out on the street, trying to pay for something in a physical store. This is where a mobile wallet comes in handy. Running as an app on your smartphone, the wallet can store the private keys for your bitcoin addresses, and enable you to pay for things directly with your phone.
In some cases, a bitcoin wallet will even take advantage of a smartphone’s near-field communication (NFC) feature, enabling you to tap the phone against a reader and pay with bitcoins without having to enter any information at all.
One common feature of mobile wallets is that they are not full bitcoin clients. A full bitcoin client has to download the entire bitcoin blockchain, which is always growing and is multiple gigabytes in size. That could get you into a heap of trouble with your mobile service provider, who will be only too happy to send you a hefty bill for downloading it over a cellular link. Many phones wouldn't be able to hold the blockchain in their memory, in any case.
Instead, these mobile clients are often designed with simplified payment verification (SPV) in mind. They download a very small subset of the blockchain, and rely on other, trusted nodes in the bitcoin network to ensure that they have the right information.
Examples of mobile wallets include the Android-based Bitcoin wallet, Mycelium, Xapo and Blockchain (which keeps your bitcoin keys encrypted on your phone, and backed up on a web-based server).
Apple is notoriously paranoid about bitcoin wallets. Coinbase had its mobile wallet app pulled from the app store altogether in November 2013, and this was followed in February 2014 by removal of Blockchain’s iOS app. However, in July 2014, bitcoin wallet apps began to reappear on the iOS store
