Cancer is a group of diseases which are characterised and actuated by somatic mutations. In cancer the distribution of mutations across the genome is inhomogeneous, with genomic and epigenomic features influencing mutational patterns. Previous studies have indicated that chromatin organization and replication time domains are correlated with and thus predictive of this variation. Here the role of alternative DNA structures was investigated across a multitude of whole-genome sequenced cancers. Sequences that are predisposed to fold in alternative DNA structures can be identified by the primary DNA sequence of the human genome and are collectively known as non-B DNA motifs. More specifically, these include Z-DNA, G-quadruplexes, inverted repeats that can fold in cruciforms and hairpins, direct and short tandem repeats that can mediate the formation of slipped structures and a subset of mirror repeats that fold in intramolecular triple stranded DNA also known as H-DNA. A systematic investigation of the association between each of those non-B DNA motifs and mutability was performed across thousands of whole genome sequenced tumours from different tissues. Non-B DNA motifs were more mutable than the surrounding regions and were found to be determinants of mutability across cancer types. Additionally, they could be used to predict variation in mutational density genome-wide. Exposed structural components and physical properties of non-B DNA motifs influenced the likelihood of mutagenesis, indicating that secondary structures are possibly causally implicated in mutagenesis. Furthermore, non-B DNA motifs increased the likelihood of recurrent mutations in the genome, which has direct implications for the identification of driver mutations in non-coding regions. A detailed characterisation of indel mutagenesis was performed across the different cancer types. The analysis indicated the roles of different non-B DNA motif categories as well as sequence homologies in indel mutagenesis. In particular, sequence characteristics of a subset of non-B DNA motifs significantly influenced their relative mutational enrichment at specific indel categories. Finally, a method was developed to quantify replication and transcription strand asymmetries at indels systematically for the first time. As a result, mutational processes that are causally implicated in strand asymmetries at indels were identified and analysed. These included mismatch repair and transcription-coupled nucleotide excision repair both of which contributed to the observed transcriptional strand asymmetries for indels.