Movement is part of all the ecosystems and most of the spatio-temporal processes. Studying movement and movement patterns aid in knowledge extraction and discovering meaningful relationships of dynamic events in our surroundings. Movement of mobile point objects, in the course of time, generates trajectories which analyzing them is highly imperative in different sciences. Among the similarity analysis approaches, detection and similarity measurement has been at focal attentions. In this regard, this research firstly investigates the concept of movement and the way a trajectory is forming. Afterward, moving spaces are presented and the pros and cons of each are outlined. In the following, similarity measurement approaches are introduced and their positive and negative features are concisely addressed. In the end, related studies which have used diverse similarity measurement approaches for various applications are surveyed comprehensively. It is hope that this research provides researchers a better understanding and perception of the process of point objects’ movement and helping them in choosing and implementing the proper similarity measurement approach.