COVID-19, a new human respiratory disease that has killed nearly 3 million people in a year since the start of the pandemic, is a global public health challenge. Its infectious agent, SARS-CoV-2, differs from other coronaviruses in a number of structural features that make this virus more pathogenic and transmissible. In this review, we discuss some important characteristics of the main SARS-CoV-2 surface antigen, the spike (S) protein, such as (i) ability of the receptor-binding domain (RBD) to switch between the "standing-up" position (open pre-fusion conformation) for receptor binding and the "lying-down" position (closed pre-fusion conformation) for immune system evasion; (ii) advantage of a high binding affinity of the RBD open conformation to the human angiotensin-converting enzyme 2 (ACE2) receptor for efficient cell entry; and (iii) S protein preliminary activation by the intracellular furin-like proteases for facilitation of the virus spreading across different cell types. We describe interactions between the S protein and cellular receptors, co-receptors, and antagonists, as well as a hypothetical mechanism of the homotrimeric spike structure destabilization that triggers the fusion of the viral envelope with the cell membrane at physiological pH and mediates the viral nucleocapsid entry into the cytoplasm. The transition of the S protein pre-fusion conformation to the post-fusion one on the surface of virions after their treatment with some reagents, such as β-propiolactone, is essential, especially in relation to the vaccine production. We also compare the COVID-19 pathogenesis with that of severe outbreaks of "avian" influenza caused by the A/H5 and A/H7 highly pathogenic viruses and discuss the structural similarities between the SARS-CoV-2 S protein and hemagglutinins of those highly pathogenic strains. Finally, we touch on the prospective and currently used COVID-19 antiviral and anti-pathogenetic therapeutics, as well as recently approved conventional and innovative COVID-19 vaccines and their molecular and immunological features.