Amplifiers and Receivers do most of the heavy lifting in your system. They process the audio portion of the signal and power your speakers. There are many different options depending on the application.
Receivers are the traditional way to handle your surround sound processing. They come in all price ranges and handle your HDMI switching and amplification in one unit.
When you have the space and the budget, separates give you the best performance. I personally believe separates are the greener choice. Amplifier technology improves over the years, but HDMI or connection changes if often what necessitates a new receiver. Separates allow you to invest in a great amplifier and change only the pre-amp in the future.
Whole House amplifiers are the heart of your distributed audio system. They come in many different types, channel configurations and power options. They can work in older volume control bassed system to newer app and voice based systems.
Network Based amplifiers can be installed to drive existing in-ceiling, bookshelf, or floor-standing speakers