Liposarcoma (LPS) is one of the most common adult soft-tissue sarcomas (STS), characterized by a high diversity of histopathological features as well as to a lesser extent by a spectrum of molecular abnormalities. Current targeted therapies for STS do not include a wide range of drugs and surgical resection is the mainstay of treatment for localized disease in all subtypes, while many LPS patients initially present with or ultimately progress to advanced disease that is either unresectable, metastatic or both. The understanding of the molecular characteristics of liposarcoma subtypes is becoming an important option for the detection of new potential targets and development novel, biology-driven therapies for this disease. Innovative therapies have been introduced and they are currently part of preclinical and clinical studies. In this review, we provide an analysis of the molecular genetics of liposarcoma followed by a discussion of the specific epigenetic changes in these malignancies. Then, we summarize the peculiarities of the key signaling cascades involved in the pathogenesis of the disease and possible novel therapeutic approaches based on a better understanding of subtype-specific disease biology. Although heterogeneity in liposarcoma genetics and phenotype as well as the associated development of resistance to therapy make difficult the introduction of novel therapeutic targets into the clinic, recently a number of targeted therapy drugs were proposed for LPS treatment. The most promising results were shown for CDK4/6 and MDM2 inhibitors as well as for the multi-kinase inhibitors anlotinib and sunitinib.