This review aims to describe epidemiological and clinical characteristics of COVID-19 in children and identify possible approaches to its therapy. We analyzed articles published in international peer-reviewed journals and official data from China, Germany, and Italy, as well as WHO reports regarding COVID-19 in children for December 2019–March 2020. The new coronavirus (SARS-CoV-2) causes disease in children of all age groups (including newborns), although it is milder than that in adults. This trend was observed during SARS-Cov-1 and MERS outbreaks. Approximately one-third of children have asymptomatic SARS-CoV-2 infection, including cases with pneumonia. Pregnant women have COVID-19 as frequently as non-pregnant women; however, vertical transmission of the virus to the fetus has not yet been confirmed or definitively rejected. We reviewed currently available information on possibilities of COVID-19 therapy in children from different age groups, depending on the disease severity. Despite the fact that most experts agree that children tend to have mild and often asymptomatic disease, there are still many factors suggesting the need for a long-term follow-up of such children, including those who had family contacts with COVID-19 patients. These factors encompass combined organ lesions, possible asymptomatic myocarditis and pneumonia in the early stages, prolonged excretion of virus particles in bodily fluids even after the elimination of the main symptoms, and uncertainty about the outcomes and consequences of the disease.