Fifth Generation (5G) is here to accelerate the digitization of economies and society, andopen up innovation opportunities for verticals. A myriad of 5G-enabled use cases has been identifiedacross disparate sectors like tourism, retail industry, and manufacturing. Many of the networks of these usecases are expected to be private networks, that is, networks intended for the exclusive use of an enterprisecustomer. This article provides an overview of the technical aspects in private 5G networks. We first identifythe key requirements and enabling solutions for private 5G networks. Then, we overview the latest 3rdGeneration Partnership Project (3GPP) Release 16 capabilities to support private 5G networks. Next, weprovide architecture proposals for single site private networks, including the scenario in which the radioaccess network (RAN) is shared. Afterwards, we address mobility and multi-site private network scenarios.Finally, we provide a summary of the key challenges for private 5G networks.