Cancer has often been described as a disease of the genome, and understanding the underlying genetics of this complex disease opens the door to developing improved treatments and more accurate diagnoses. The abundant availability of next-generation DNA sequencing data in recent years has provided a tremendous opportunity to enhance our understanding of cancer genetics. Despite having this wealth of data available, analyzing tumor DNA data is complicated by issues such as genetic heterogeneity often found in tumor tissue samples, and the diverse and complex genetic landscape that is characteristic of tumors. Advanced computational analysis techniques are required in order to address these challenges and to deal with the enormous size and inherent complexity of tumor DNA data. The focus of this thesis is to develop novel computational techniques to analyze tumor DNA data and address several ongoing challenges in the area of cancer genomics research. These techniques are organized into three main aims or focuses. The first focus is on developing algorithms to detect patterns of co-occurring mutations associated with tumor formation in insertional mutagenesis data. Such patterns can be used to enhance our understanding of cancer genetics, as well as to identify potential targets for therapy. The second focus is on assembling personal genomic sequences from tumor DNA. Personal genomic sequences can enhance the efficacy of downstream analyses that measure gene expression or regulation, especially for tumor cells. The final focus is on estimating variant frequencies from heterogeneous tumor tissue samples. Accounting for heterogeneous variants is essential when analyzing tumor samples, as they are often the cause of therapy resistance and tumor recurrence in cancer.