With the increasing demand for digital video applications in our daily lives, video coding and decoding become critical tasks that must be supported by several types of devices and systems. This paper presents a discussion of the main challenges to design dedicated hardware architectures based on modern hybrid video coding formats, such as the High Efficiency Video Coding (HEVC), the AOMedia Video 1 (AV1) and the Versatile Video Coding (VVC). The paper discusses eachstep of the hybrid video coding process, highlighting the main challenges for each codec and discussing the main hardware solutions published in the literature. The discussions presented in the paper show that there are still many challenges to be overcome and open research opportunities, especially for the AV1 and VVC codecs. Most of these challenges are related to the high throughput required for processing high and ultrahigh resolution videos in real time and to energy constraints of multimedia-capable devices.