COVID-19, which is caused by SARS-CoV-2, can result in acute respiratory distress syndrome and multiple organ failure^{, , –}, but little is known about its pathophysiology. Here we generated single-cell atlases of 24 lung, 16 kidney, 16 liver and 19 heart autopsy tissue samples and spatial atlases of 14 lung samples from donors who died of COVID-19. Integrated computational analysis uncovered substantial remodelling in the lung epithelial, immune and stromal compartments, with evidence of multiple paths of failed tissue regeneration, including defective alveolar type 2 differentiation and expansion of fibroblasts and putative TP63⁺ intrapulmonary basal-like progenitor cells. Viral RNAs were enriched in mononuclear phagocytic and endothelial lung cells, which induced specific host programs. Spatial analysis in lung distinguished inflammatory host responses in lung regions with and without viral RNA. Analysis of the other tissue atlases showed transcriptional alterations in multiple cell types in heart tissue from donors with COVID-19, and mapped cell types and genes implicated with disease severity based on COVID-19 genome-wide association studies. Our foundational dataset elucidates the biological effect of severe SARS-CoV-2 infection across the body, a key step towards new treatments.