Osteosarcoma is a genomically complex disease characterized by few recurrent single-nucleotide mutations or in-frame fusions. In contrast, structural alterations, including copy number changes, chromothripsis, kataegis, loss of heterozygosity (LOH), and other large-scale genomic alterations, are frequent and widespread across the osteosarcoma genome. These observed structural alterations lead to activation of oncogenes and loss of tumor suppressors which together contribute to oncogenesis. To date, few targeted therapies for osteosarcoma have been identified. It is likely that effectiveness of targeted therapies will vary greatly in subsets of tumors with distinct key driver events. Model systems which can recapitulate the genetic heterogeneity of this disease are needed to test this hypothesis. One possible approach is to use patient-derived xenograft (PDX) models characterized with regards to their similarity to the human tumor samples from which they were derived. Here we review evidence pointing to the genomic complexity of osteosarcoma and how this is reflected in available model systems. We also review the current state of preclinical testing for targeted therapies using these models.