Malignant pleural mesothelioma (MPM) is a lethal thoracic malignancy whose incidence is still increasing worldwide. MPM is characterized by frequent inactivation of tumor-suppressor genes (TSGs), e.g., the homozygous deletion of CDKN2A/2B and various genetic alterations that inactivate BAP1, NF2, LATS1/2, and TP53. The leading cause for the poor prognosis of patients with MPM is the lack of effective treatment options, with conventional chemotherapy being the standard of care in the clinic, which has remained unchanged for almost 20 years. Precision oncology, a burgeoning effort to provide precise cancer treatment tailored to unique molecular changes in individual patients, has made tremendous progress in the last decade in several cancers, but not in MPM. Recent studies indicate a high degree of tumor heterogeneity in MPM and the importance to optimize histological and molecular classifications for improved treatment. In this review, we provide an up-to-date overview of recent advances in MPM by focusing on new stratifications of tumor subgroups, specific vulnerabilities associated with functional loss of TSGs and other biomarkers, and potential clinical implications. The molecularly based subdivisions not only deepen our understanding of MPM pathobiology, but more importantly, they may raise unprecedented new hopes for personalized treatment of MPM patients with biomarker-guided targeted and immunotherapies.