The study of galaxy protoclusters is beginning to fill in unknown details of the important phase of the assembly of clusters and cluster galaxies. This review describes the current status of this field and highlights promising recent findings related to galaxy formation in the densest regions of the early universe. We discuss the main search techniques and the characteristic properties of protoclusters in observations and simulations, and show that protoclusters will have present-day masses similar to galaxy clusters when fully collapsed. We discuss the physical properties of galaxies in protoclusters, including (proto-)brightest cluster galaxies, and the forming red sequence. We highlight the fact that the most massive halos at high redshift are found in protoclusters, making these objects uniquely suited for testing important recent models of galaxy formation. We show that galaxies in protoclusters should be among the first galaxies at high redshift making the transition from a gas cooling regime dominated by cold streams to a regime dominated by hot intracluster gas, which could be tested observationally. We also discuss the possible connections between protoclusters and radio galaxies, quasars, and Ly-alpha blobs. Because of their early formation, large spatial sizes and high total star formation rates, protoclusters have also likely played a crucial role during the epoch of reionization, which can be tested with future experiments that will map the neutral and ionized cosmic web. Last, we review a number of promising observational projects that are expected to make significant impact in this growing, exciting field.
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