This topical review addresses how semiconductor systems may reveal scalable properties similar to those known from Rydberg atoms and in which ways they may be utilized for precision sensing and to realize huge long-range interactions in semiconductor systems. Due to the interdisciplinary nature of the field, it has a twofold purpose: First, it may serve as an introduction to Rydberg physics for semiconductor physicists unfamiliar with the topic. Second, it may also serve as an overview of the specific opportunities and challenges arising in semiconductor physics for researchers who are familiar with Rydberg physics of cold atom gases, but new to the field of semiconductor physics. The review starts with an introduction on the general properties of excitons in semiconductors. Then, the material system Cu2O, which is the best developed platform for semiconductor Rydberg physics at the moment, is discussed in detail.