Cancer is a genetic disease due to the accumulation of numerous mutations rendering the tumour cell insensitive to control by the local cellular environment and by the whole organism. Analysis of the frequency of appearance of human cancer as a function of age shows that between four and seven mutations in key genes are usually necessary to produce most human cancers. Interesting debates in the literature are concerned with the idea that normal mutation rates followed by selective advantage of mutated clones are enough to produce the numerous mutations found in human cancers. Alternatively, the mutator phenotype hypothesis is based on the idea that the normal mutation rates are insufficient to account for the multiple mutations found in tumours. It is, however, difficult not only to know this exact mutation frequency in cells but also to know the total number of cell divisions giving rise to a cancer. Therefore, during at least one step in the carcinogenic process, a mutator phenotype in target cells may occur due to mutations controlling the fidelity of DNA replication or DNA repair, the apoptosis pathways or the cell cycle checkpoint regulations. Among the multiple mutations found in human cancers such as gene amplification, chromosome alterations and translocations, point mutations are very important and the molecular mechanisms of their production are well documented. I will describe in detail the various mechanisms that a cell can use to produce point mutations due to lower fidelity in the DNA polymerisation step or to inefficient repair pathways. The presence of multiple mutations in human cancer is interesting not only in terms of understanding the carcinogenesis process in humans but also in eventually promoting strategies to decrease the efficiency of this process and to increase cancer therapy regimen.