We have examined genome sequences of thousands of tumors (of various cancer types) to search for unusual patterns in how mutations are distributed in the genome. This has led to a finding of the so-called ‘mutation fog’: a clustering pattern that reflects how sometimes the cellular DNA repair systems can, erroneously, start introducing mutations instead of correcting them (published as Mas-Ponte & Supek, Nature Genetics, 2020). This may help explain the differences in cancer propensity across individuals and across human tissues. Next, we have examined a different kind of pattern: the density of mutations distributed across large swaths (a million nucleotides) of the human chromosomes. Remarkably this pattern allows a very accurate classification of tumors into tissues and subtypes, starting only from the mutational pattern (published as Salvadores, Mas-Ponte and Supek, PLOS Computational BIology, 2019), without necessity to consult e.g. gene expression data -- a standard tool for cancer typing. This opens new avenues for diagnosing cancer type by DNA sequencing from ‘liquid biopsies’ (cancer cells or cancer DNA in blood plasma), and for classifying the metastatic ‘cancers of unknown origin’. Furthermore, we have examined how increased mutation burden of so-called ‘nonsense’ mutations affects human cells including tumors, which have a special mechanism (NMD) that degrades genetic messages containing nonsense mutations. We found that this NMD mechanism dampens the results of cancer immunotherapy in many cancer patients, and that it can be predicted from the genome sequence of tumors which patients those are (Lindeboom, Vermeulen, Lehner & Supek, 2019, Nature Genetics). Our data strongly suggest pharmacological NMD inhibition could be used to potentiate tumor immunotherapy, guided by genomic markers. Finally, we have analysed diverse mutation patterns (together with gene expression patterns and epigenomic patterns) occurring in tumor cell lines -- an experimental model of tumor biology, which is used by many labs around the world to test new cancer therapies. We found, suprisingly, that approximately 6% of all cancer cell lines may originate from a different tissue than originally thought, as classified by the mutational and gene regulation patterns, using a machine learning method (Salvadores, Fuster and Supek, 2020, Science Advances). This has important implications for experimentally testing new cancer therapies in cancer cell lines, because the tissue-of-origin has a strong effect on how the cancer cell lines respond to drugs. Overall, our work suggests that examining mutational patterns in human cancer cells can provide new insight into carcinogenesis and also new avenues for treating cancer.