COVID-19 has resulted in huge numbers of infections and deaths worldwide and brought the most severe disruptions to societies and economies since the Great Depression. Massive experimental and computational research effort to understand and characterize the disease and rapidly develop diagnostics, vaccines, and drugs has emerged in response to this devastating pandemic and more than 130 000 COVID-19-related research papers have been published in peer-reviewed journals or deposited in preprint servers. Much of the research effort has focused on the discovery of novel drug candidates or repurposing of existing drugs against COVID-19, and many such projects have been either exclusively computational or computer-aided experimental studies. Herein, we provide an expert overview of the key computational methods and their applications for the discovery of COVID-19 small-molecule therapeutics that have been reported in the research literature. We further outline that, after the first year the COVID-19 pandemic, it appears that drug repurposing has not produced rapid and global solutions. However, several known drugs have been used in the clinic to cure COVID-19 patients, and a few repurposed drugs continue to be considered in clinical trials, along with several novel clinical candidates. We posit that truly impactful computational tools must deliver actionable, experimentally testable hypotheses enabling the discovery of novel drugs and drug combinations, and that open science and rapid sharing of research results are critical to accelerate the development of novel, much needed therapeutics for COVID-19.