Motion capture technologies digitize human movements by tracking 3D positions of specific skeleton joints in time. Such spatio-temporal data have an enormous application potential in many fields, ranging from computer animation, through security and sports to medicine, but their computerized processing is a difficult problem. The recorded data can be imprecise, voluminous, and the same movement action can be performed by various subjects in a number of alternatives that can vary in speed, timing or a position in space. This requires employing completely different data-processing paradigms compared to the traditional domains such as attributes, text or images. The objective of this tutorial is to explain fundamental principles and technologies designed for similarity comparison, searching, subsequence matching, classification and action detection in the motion capture data. Specifically, we emphasize the importance of similarity needed to express the degree of accordance between pairs of motion sequences and also discuss the machine-learning approaches able to automatically acquire content-descriptive movement features. We explain how the concept of similarity together with the learned features can be employed for searching similar occurrences of interested actions within a long motion sequence. Assuming a user-provided categorization of example motions, we discuss techniques able to recognize types of specific movement actions and detect such kinds of actions within continuous motion sequences. Selected operations will be demonstrated by on-line web applications.