Collective phenomena and their associated movement patterns are ubiquitous in everyday life. However, formal reasoning about these phenomena is currently hampered by the lack of adequate tools. We have previously developed a classification of collectives but this is incomplete with regards to movement and therefore needs to be integrated with a classification of collective motion. This paper analyses existing research into the movement patterns of collectives. Although there has been some research into the movement patterns of particular kinds of collectives, most of this is found to focus on the level of the individuals; vital information about the collective is lost. Existing research that focuses on movement patterns improves on this but still leaves many questions unanswered and important features of collectives unable to be represented. Therefore, we develop a list of goals which we believe a classification of collective motion needs to satisfy, and introduce the foundations of a system that we believe will satisfy these goals. We hope that this work will provide a sound basis for the development and formalisation of a comprehensive classification of collectives and their motions.