A user gestures with a wireless mobile phone device to control some aspect of its operation, or the operation of a remote system with which the device communicates. Application programs can solicit gestural information through a standardized set of interface protocols (e.g., API functions). One function, for example, solicits a running set of gesture data, and a complementary function discontinues the first function. Other functions solicit device movement data in particular directions. In some arrangements gesture data is sent by the wireless device to a remote system, which may issue a response that is dependent on the received gesture data. This response may also depend on other data obtained by the wireless device (e.g., obtained from an electronic or physical object, or sensed from the environment) and sent to the remote system. The wireless device may have different modes of interacting with users, to accommodate users with greater or lesser proficiency in gestural techniques. A variety of other features and arrangements are also detailed.