Recent advances in natural language question-answering systems and context-aware mobile apps create opportunities for improved sensemaking in a tactical setting. Users equipped with mobile devices act as both sensors (able to acquire information) and effectors (able to act in situ), operating alone or in collectives. The currently-dominant technical approaches follow either a pull model (e.g. Apple"s Siri or IBM"s Watson which respond to users" natural language queries) or a push model (e.g. Google"s Now which sends notifications to a user based on their context). There is growing recognition that users need more flexible styles of conversational interaction, where they are able to freely ask or tell, be asked or told, seek explanations and clarifications. Ideally such conversations should involve a mix of human and machine agents, able to collaborate in collective sensemaking activities with as few barriers as possible. Desirable capabilities include adding new knowledge, collaboratively building models, invoking specific services, and drawing inferences. As a step towards this goal, we collect evidence from a number of recent pilot studies including natural experiments (e.g. situation awareness in the context of organised protests) and synthetic experiments (e.g. human and machine agents collaborating in information seeking and spot reporting). We identify some principles and areas of future research for "conversational sensemaking"'.