Cancer is an umbrella term that includes a wide spectrum of disease severity, from those that are malignant, metastatic, and aggressive to benign lesions with very low potential for progression or death. The ability to prognosticate patient outcomes would facilitate management of various malignancies: patients whose cancer is likely to advance quickly would receive necessary treatment that is commensurate with the predicted biology of the disease. Former prognostic models based on clinical variables (age, gender, cancer stage, tumor grade, etc.), though helpful, cannot account for genetic differences, molecular etiology, tumor heterogeneity, and important host biological mechanisms. Therefore, recent prognostic models have shifted toward the integration of complementary information available in both molecular data and clinical variables to better predict patient outcomes: vital status (overall survival), metastasis (metastasis-free survival), and recurrence (progression-free survival). In this article, we review 20 survival prediction approaches that integrate multi-omics and clinical data to predict patient outcomes. We discuss their strategies for modeling survival time (continuous and discrete), the incorporation of molecular measurements and clinical variables into risk models (clinical and multi-omics data), how to cope with censored patient records, the effectiveness of data integration techniques, prediction methodologies, model validation, and assessment metrics. The goal is to inform life scientists of available resources, and to provide a complete review of important building blocks in survival prediction. At the same time, we thoroughly describe the pros and cons of each methodology, and discuss in depth the outstanding challenges that need to be addressed in future method development.