The exponential growth of digital data sources, such as those enabled by the IoT, coupled with the ubiquity of non-trivial computational power, at the edges, in the core and in-between, for processing this data have the potential for fundamentally transforming our ability to understand and manage our lives and our environment. However, to achieve this impact data must be processed in a timely manner to extract critical insights that can drive decision making. In this talk I will explore data-driven online computing in the continuum – a paradigm that opportunistically aggregates distributed resources and services at the edges, in the core and along the data path, to process data in-situ and in-transit and support emerging data-driven workflows. Realizing this paradigm requires novel solutions for federating infrastructure, programming applications and services, and composing dynamic workflows, which are capable of reacting in real-time to unpredictable data sizes, availabilities, locations, and rates. Using examples from our work in the CometCloud project, I will present research challenges as well as some initial solutions towards realizing this paradigm.