Communication within groups of agents has been lately the focus of research in dynamic epistemic logic. This paper studies a recently introduced form of partial (more precisely, topic-based) communication. This type of communication allows for modelling scenarios of multi-agent collaboration and negotiation, and it is particularly well-suited for situations in which sharing all information is not feasible/advisable. The paper can be divided into two parts. In the first part, we present results on invariance and complexity of model checking. Moreover, we (...) compare partial communication with the public announcement and arrow update settings in terms of both language-expressivity and update-expressivity. Regarding the former, the three settings are equivalent, their languages being equally expressive. Regarding the latter, all three modes of communication are incomparable in terms of update-expressivity. In the second part, we shift our attention to strategic topic-based communication. We do so by extending the language with a modality that quantifies over the topics the agents can ‘talk about’, thus allowing a form of arbitrary partial communication. For this new framework, we provide a complete axiomatisation, showing also that the new language’s model checking problem is PSPACE-complete. Finally, we argue that, in terms of expressivity, this new language of arbitrary partial communication is incomparable to that of arbitrary public announcements and also to that of arbitrary arrow updates. (shrink)