Wearable smart devices, such as smart watch, wristband are becoming increasingly popular recently. They generally integrate the MEMS-designed inertial sensors, including accelerometer, gyroscope and compass, which provide a convenient and inexpensive way to collect motion data of users. Such rich, continuous motion data provide great potential for remote healthcare and decease diagnosis. Information processing algorithms play the critical role in these approaches, which is to extract the motion signatures and to access different kinds of judgements. This paper reviews key algorithms in these areas. In particular, we focus on three kinds of applications: 1) gait analysis; 2) fall detection and 3) sleep monitoring. They are the most popular healthcare applications based on the inertial data. By categorizing and introducing the key algorithms, this paper tries to build a clear map of how the inertial data are processed; how the inertial signatures are defined, extracted, and utilized in different kinds of applications. This will provide a valuable guidance for users to understand the methodologies and to select proper algorithm for specific application purpose.