P colonies are abstract computing devices modelling communities of very simple reactive agents living and acting in a joint shared environment. The concept was motivated by so-called colonies, grammar systems based on interplay of very simple agents, on one hand, and by membrane systems, massively parallel computational models inspired by cell biology, on the other hand. Some variants of P colonies also allow the environment to participate actively in the system's evolution. In this paper we summarize the most important results on P colonies, present open problems concerning these constructs, and suggest new research directions in their study.