The new disease produced by severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) represents a major pandemic event nowadays. Since its origin in China in December 2019, there is compelling evidence that novel SARS-CoV-2 is a highly transmissible virus, and it is associated to a broad clinical spectrum going from subclinical presentation to severe respiratory distress and multiorgan failure. Like other coronaviruses, SARS-CoV-2 recognizes human angiotensin-converting enzyme 2 as a cellular receptor that allows it to infect different host cells and likely disrupts renin-angiotensin-aldosterone system homeostasis. Particularly, a considerable incidence of many renal abnormalities associated to COVID-19 has been reported, including proteinuria, hematuria, and acute kidney injury. Moreover, it has been recently demonstrated that SARS-CoV-2 can infect podocytes and tubular epithelial cells, which could contribute to the development of the aforementioned renal abnormalities. In this review, we discuss the biological aspects of SARS-CoV-2 infection, how understanding current knowledge about SARS-CoV-2 infection may partly explain the involvement of the kidneys in the pathophysiology of COVID-19, and what questions have arisen and remain to be explored.