The domains of complex event processing (CEP) and business process management (BPM) have different origins but for many aspects draw on similar concepts. While specific combinations of BPM and CEP have attracted research attention, resulting in solutions to specific problems, we attempt to take a broad view at the opportunities and challenges involved. We first illustrate these by a detailed example from the logistics domain. We then propose a mapping of this area into four quadrants – two quadrants drawing from CEP to create or extend process models and two quadrants starting from a process model to address how it can guide CEP. Existing literature is reviewed and specific challenges and opportunities are indicated for each of these quadrants. Based on this mapping, we identify challenges and opportunities that recur across quadrants and can be considered as the core issues of this combination. We suggest that addressing these issues in a generic manner would form a sound basis for future applications and advance this area significantly.