The Big Data challenge has made the issue of "making sense" of data urgent and unavoidable. This paper introduces exploratory computing (EC), a novel paradigm whose aim is to support a comprehensive "exploratory" experience for the user. "Exploratory" because it supports search and discovery of information through various tasks (investigation, knowledge seeking, serendipitous discovery, comparison of information…) in a dynamic interaction, where meaningful feedbacks from the system play a crucial role, closely resembling a human-to-human dialogue. "Computing" because a complex interaction as the one outlined above requires powerful computational strength for the user to be able to fully profit from, and even enjoy, the interaction. EC is not associated with a predefined set of techniques: Rather, it is an approach that can be concretized in different ways. In the paper, two different implementations of the EC approach are presented, both of which interpret the EC highlevel requirements. It is the authors' hope that others will follow.