Invasive fungal infections (IFIs) can complicate the clinical course of COVID-19 and are associated with a significant increase in mortality, especially in critically ill patients admitted to an intensive care unit (ICU). This narrative review concerns 4099 cases of IFIs in 58,784 COVID-19 patients involved in 168 studies. COVID-19-associated invasive pulmonary aspergillosis (CAPA) is a diagnostic challenge because its non-specific clinical/imaging features and the fact that the proposed clinically diagnostic algorithms do not really apply to COVID-19 patients. Forty-seven observational studies and 41 case reports have described a total of 478 CAPA cases that were mainly diagnosed on the basis of cultured respiratory specimens and/or biomarkers/molecular biology, usually without histopathological confirmation. Candidemia is a widely described secondary infection in critically ill patients undergoing prolonged hospitalisation, and the case reports and observational studies of 401 cases indicate high crude mortality rates of 56.1% and 74.8%, respectively. COVID-19 patients are often characterised by the presence of known risk factors for candidemia such as in-dwelling vascular catheters, mechanical ventilation, and broad-spectrum antibiotics. We also describe 3185 cases of mucormycosis (including 1549 cases of rhino-orbital mucormycosis (48.6%)), for which the main risk factor is a history of poorly controlled diabetes mellitus (>76%). Its diagnosis involves a histopathological examination of tissue biopsies, and its treatment requires anti-fungal therapy combined with aggressive surgical resection/debridement, but crude mortality rates are again high: 50.8% in case reports and 16% in observational studies. The presence of other secondary IFIs usually diagnosed in severely immunocompromised patients show that SARS-CoV-2 is capable of stunning the host immune system: 20 cases of Pneumocystis jirovecii pneumonia, 5 cases of cryptococcosis, 4 cases of histoplasmosis, 1 case of coccidioides infection, 1 case of pulmonary infection due to Fusarium spp., and 1 case of pulmonary infection due to Scedosporium.