Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is the third (following SARS-CoV and Middle East Respiratory Syndrome-CoV) zoonotic coronavirus that has crossed the species barrier in the 21st century, resulting in the development of serious human infection. The punishing effect of the recent outbreak of pandemic disease termed COVID-19 (coronavirus disease-19) caused by SARS-CoV-2 impelled us to gather the facts about the nature of coronaviruses. First, we introduce the basic information about coronavirus taxonomy, structure, and replication process to create the basis for more advanced consideration. In the following part of this review, we focused on interactions between the virus and the receptor on the host cell, as this stage is the critical process determining the species and tissue tropism, as well as clinical course of infection. We also illuminate the molecular basis of the strategy used by coronaviruses to cross the species barrier. We give special attention to the cellular receptor's interaction with S protein of different CoVs (dipeptidyl peptidase IV and angiotensin-converting enzyme 2), as well as the cellular proteases involved in proteolysis of this protein. These factors determine the virus entry and replication; thus, even fine quantitative or qualitative differences in their expression may crucially affect outcomes of infection. Understanding virus biology and characterization of the host factors involved in coronavirus transmission and pathogenesis may offer novel options for development of efficient therapeutic and preventive strategies.