The COVID-19 pandemic rapidly spread around the world following the first reports in Wuhan City, China in late 2019. The disease, caused by the novel SARS-CoV-2 virus, is primarily a respiratory condition that can affect numerous other bodily systems including the cardiovascular and gastrointestinal systems. The disease ranges in severity from asymptomatic through to severe acute respiratory distress requiring intensive care treatment and mechanical ventilation, which can lead to respiratory failure and death. It has rapidly become evident that COVID-19 patients can develop features of interstitial pulmonary fibrosis, which in many cases persist for as long as we have thus far been able to follow the patients. Many questions remain about how such fibrotic changes occur within the lung of COVID-19 patients, whether the changes will persist long term or are capable of resolving, and whether post-COVID-19 pulmonary fibrosis has the potential to become progressive, as in other fibrotic lung diseases. This review brings together our existing knowledge on both COVID-19 and pulmonary fibrosis, with a particular focus on lung epithelial cells and fibroblasts, in order to discuss common pathways and processes that may be implicated as we try to answer these important questions in the months and years to come.