In-network computing using programmable networking hardware is a strong trend in networking that promises to reduce latency and consumption of server resources through offloading to network elements (programmable switches and smart NICs). In particular, the data plane programming language P4 together with powerful P4 networking hardware has spawned projects offloading services into the network, e.g., consensus services or caching services. In this paper, we present a novel case for in-network computing, namely, Complex Event Processing (CEP). CEP processes streams of basic events, e.g., stemming from networked sensors, into meaningful complex events. Traditionally, CEP processing has been performed on servers or overlay networks. However, we argue in this paper that CEP is a good candidate for in-network computing along the communication path avoiding detouring streams to distant servers to minimize communication latency while also exploiting processing capabilities of novel networking hardware. We show that it is feasible to express CEP operations in P4 and also present a tool to compile CEP operations, formulated in our P4CEP rule specification language, to P4 code. Moreover, we identify challenges and problems that we have encountered to show future research directions for implementing full-fledged in-network CEP systems.