Metastasis is the main cause of death in patients with cancer. The molecular mechanisms underlying the different metastasis steps are not yet fully known, partly because most studies have been focusing only on cancer cells within the tumor. Currently, with the development of technologies for the enrichment and capture of circulating tumor cells (CTCs), it is possible to characterize cancer cells at the exact moment of metastasis initiation. Therefore, CTCs are a promising bio-source for real-time liquid biopsies in patients with cancer. However, their exploitation has been hampered by the limited number of CTCs in the bloodstream and the changing phenotype of cancer cells during the metastatic process. Different methods have been developed to expand CTCs in vitro and in vivo (in animal models) with the aim of characterizing functional metastasis-initiator CTCs with stemness traits, and to obtain new diagnostics and therapeutic tools. In this review, we describe how the establishment of in vitro CTC cultures and of CTC-derived xenografts has led to the identification of molecular mechanisms related to metastasis initiation by CTCs, such as epithelial-to-mesenchymal transition (EMT), stemness, and clustering. These models enable the functional analysis and in-depth proteomic, transcriptomic and genomic profiling of metastasis-competent CTCs. We then discuss the relationship between EMT and stem cell features, and how these aspects might interact with other factors in the tumor microenvironment to induce CTC dissemination and proliferation in distant organs.