In recent years, substantial progress has been made in the field of reverberant speech signal processing, including both single-and multichannel dereverberation techniques and automatic speech recognition (ASR) techniques that are robust to reverberation. In this paper, we describe the REVERB challenge, which is an evaluation campaign that was designed to evaluate such speech enhancement (SE) and ASR techniques to reveal the state-of-the-art techniques and obtain new insights regarding potential future research directions. Even though most existing benchmark tasks and challenges for distant speech processing focus on the noise robustness issue and sometimes only on a single-channel scenario, a particular novelty of the REVERB challenge is that it is carefully designed to test robustness against reverberation, based on both real, single-channel, and multichannel recordings. This challenge attracted 27 papers, which represent 25 systems specifically designed for SE purposes and 49 systems specifically designed for ASR purposes. This paper describes the problems dealt within the challenge, provides an overview of the submitted systems, and scrutinizes them to clarify what current processing strategies appear effective in reverberant speech processing.