Invasive pulmonary aspergillosis (IPA) is increasingly recognized as a life-threatening superinfection of severe respiratory viral infections, such as influenza. The pandemic of Coronavirus Disease 2019 (COVID-19) due to emerging SARS-CoV-2 rose concern about the eventuality of IPA complicating COVID-19 in intensive care unit mechanically-ventilated patients. While the association between severe influenza and IPA has been demonstrated, it remains unclear whether SARS-CoV-2 infection represents a specific risk factor for IPA. A variable incidence of such complication has been previously reported, which can be partly attributed to differences in diagnostic strategy and IPA definitions, and possibly local environmental/epidemiological factors. In this article, we discuss the similarities and differences between influenza-associated pulmonary aspergillosis (IAPA) and COVID-19-associated pulmonary aspergillosis (CAPA). Compared to IAPA, the majority of CAPA cases have been classified as putative rather than proven/probable IPA, in the absence of positive serum galactomannan or histopathologic evidence of angio-invasion. Discrimination between Aspergillus airways colonization and CAPA is difficult. Distinct physiopathology and cytokine profiles of influenza and COVID-19 may explain these discrepancies. Whether CAPA represents a distinct entity is still debatable and many questions remain unanswered, such as its actual incidence, the predisposing role of corticosteroids or immunomodulatory drugs, and the indications for antifungal therapy.