Rapidly appearing SARS-CoV-2 mutations can affect T cell epitopes, which can help the virus to evade either CD8 or CD4 T-cell responses. We developed T-cell COVID-19 Atlas (T-CoV, https://t-cov.hse.ru) – the comprehensive web portal, which allows one to analyze how SARS-CoV-2 mutations alter the presentation of viral peptides by HLA molecules. The data are presented for common virus variants and the most frequent HLA class I and class II alleles. Binding affinities of HLA molecules and viral peptides were assessed with accurate in silico methods. The obtained results highlight the importance of taking HLA alleles diversity into account: mutation-mediated alterations in HLA-peptide interactions were highly dependent on HLA alleles. For example, we found that the essential number of peptides tightly bound to HLA-B*07:02 in the reference Wuhan variant ceased to be tight binders for the Indian (Delta) and the UK (Alpha) variants. In summary, we believe that T-CoV will help researchers and clinicians to predict the susceptibility of individuals with different HLA genotypes to infection with variants of SARS-CoV-2 and/or forecast its severity.