Natural products with polypharmacological profiles have demonstrated promise as novel therapeutics for various complex diseases, including cancer. Currently, many gaps exist in our knowledge of which compounds interact with which targets, and experimentally testing all possible interactions is infeasible. Recent advances and developments of systems pharmacology and computational (in silico) approaches provide powerful tools for exploring the polypharmacological profiles of natural products. In this review, we introduce recent progresses and advances of computational tools and systems pharmacology approaches for identifying drug targets of natural products by focusing on the development of targeted cancer therapy. We survey the polypharmacological and systems immunology profiles of five representative natural products that are being considered as cancer therapies. We summarize various chemoinformatics, bioinformatics and systems biology resources for reconstructing drug-target networks of natural products. We then review currently available computational approaches and tools for prediction of drug-target interactions by focusing on five domains: target-based, ligand-based, chemogenomics-based, network-based and omics-based systems biology approaches. In addition, we describe a practical example of the application of systems pharmacology approaches by integrating the polypharmacology of natural products and large-scale cancer genomics data for the development of precision oncology under the systems biology framework. Finally, we highlight the promise of cancer immunotherapies and combination therapies that target tumor ecosystems (e.g. clones or 'selfish' sub-clones) via exploiting the immunological and inflammatory 'side' effects of natural products in the cancer post-genomics era.