Age is the most important risk factor for cancer, as cancer incidence and mortality increase with age. However, how molecular alterations in tumours differ among patients of different age remains largely unexplored. Here, using data from The Cancer Genome Atlas, we comprehensively characterise genomic, transcriptomic and epigenetic alterations in relation to patients' age across cancer types. We show that tumours from older patients present an overall increase in genomic instability, somatic copy-number alterations (SCNAs) and somatic mutations. Age-associated SCNAs and mutations are identified in several cancer-driver genes across different cancer types. The largest age-related genomic differences are found in gliomas and endometrial cancer. We identify age-related global transcriptomic changes and demonstrate that these genes are in part regulated by age-associated DNA methylation changes. This study provides a comprehensive, multi-omics view of age-associated alterations in cancer and underscores age as an important factor to consider in cancer research and clinical practice.