A main goal of Precision Medicine is that of incorporating and integrating the vast corpora on different databases about the molecular and environmental origins of disease, into analytic frameworks, allowing the development of individualized, context-dependent diagnostics, and therapeutic approaches. In this regard, artificial intelligence and machine learning approaches can be used to build analytical models of complex disease aimed at prediction of personalized health conditions and outcomes. Such models must handle the wide heterogeneity of individuals in both their genetic predisposition and their social and environmental determinants. Computational approaches to medicine need to be able to efficiently manage, visualize and integrate, large datasets combining structure, and unstructured formats. This needs to be done while constrained by different levels of confidentiality, ideally doing so within a unified analytical architecture. Efficient data integration and management is key to the successful application of computational intelligence approaches to medicine. A number of challenges arise in the design of successful designs to medical data analytics under currently demanding conditions of performance in personalized medicine, while also subject to time, computational power, and bioethical constraints. Here, we will review some of these constraints and discuss possible avenues to overcome current challenges.