Patient-derived tumor xenografts (PDXs), in which tumor fragments surgically dissected from cancer patients are directly transplanted into immunodeficient mice, have emerged as a useful model for translational research aimed at facilitating precision medicine. PDX susceptibility to anti-cancer drugs is closely correlated with clinical data in patients, from whom PDX models have been derived. Accumulating evidence suggests that PDX models are highly effective in predicting the efficacy of both conventional and novel anti-cancer therapeutics. This also allows “co-clinical trials,” in which pre-clinical investigations in vivo and clinical trials could be performed in parallel or sequentially to assess drug efficacy in patients and PDXs. However, tumor heterogeneity present in PDX models and in the original tumor samples constitutes an obstacle for application of PDX models. Moreover, human stromal cells originally present in tumors dissected from patients are gradually replaced by host stromal cells as the xenograft grows. This replacement by murine stroma could preclude analysis of human tumor-stroma interactions, as some mouse stromal cytokines might not affect human carcinoma cells in PDX models. The present review highlights the biological and clinical significance of PDX models and three-dimensional patient-derived tumor organoid cultures of several kinds of solid tumors, such as those of the colon, pancreas, brain, breast, lung, skin, and ovary.