The infectious coronavirus disease (COVID-19) pandemic, caused by the coronavirus SARS-CoV-2, appeared in December 2019 in Wuhan, China, and has spread worldwide. As of today, more than 22 million people have been infected, with almost 800,000 fatalities. With the purpose of contributing to the development of effective therapeutics, this work provides an overview of the viral machinery and functional role of each SARS-CoV-2 protein, and a thorough analysis of the structure and druggability assessment of the viral proteome. All structural, non-structural, and accessory proteins of SARS-CoV-2 have been studied, and whenever experimental structural data of SARS-CoV-2 proteins were not available, homology models were built based on solved SARS-CoV structures. Several potential allosteric or protein-protein interaction druggable sites on different viral targets were identified, knowledge that could be used to expand current drug discovery endeavors beyond the cysteine proteases and the polymerase complex. It is our hope that this study will support the efforts of the scientific community both in understanding the molecular determinants of this disease and in widening the repertoire of viral targets in the quest for repurposed or novel drugs against COVID-19.