Trends in hardware, the prevalence of the cloud, and the rise of highly demanding applications have ushered an era of specialization that quickly changes how data is processed at scale. These changes are likely to continue and accelerate in the next years as new technologies are adopted and deployed: smart NICs, smart storage, smart memory, disaggregated storage, disaggregated memory, specialized accelerators (GPUS, TPUs, FPGAs), and a wealth of ASICs specifically created to deal with computationally expensive tasks (e.g., cryptography or compression). In this tutorial, we focus on data processing on FPGAs, a technology that has received less attention than, e.g., TPUs or GPUs but that is, however, increasingly being deployed in the cloud for data processing tasks due to the architectural flexibility of FPGAs, along with their ability to process data at line rate, something not possible with other types of processors or accelerators. In the tutorial, we will cover what FPGAs are, their characteristics, their advantages and disadvantages, as well as examples from deployments in the industry and how they are used in various data processing tasks. We will introduce FPGA programming with high-level languages and describe hardware and software resources available to researchers. The tutorial includes case studies borrowed from research done in collaboration with companies that illustrate the potential of FPGAs in data processing and how software and hardware are evolving to take advantage of the possibilities offered by FPGAs. The use cases include: (1) approximated nearest neighbor search, which is relevant to databases and machine learning, (2) remote disaggregated memory, showing how the cloud architecture is evolving and demonstrating the potential for operator offloading and line rate data processing, and (3) recommendation system as an application with tight latency constraints.