In recent years, the tissue engineering paradigm has shifted to include a new and growing subfield of scaffoldless techniques that generate self-organizing and self-assembling tissues. This review aims to cogently describe this relatively new research area, with special focus on applications toward clinical use and research models. Particular emphasis is placed on providing clear definitions of self-organization and the self-assembling process, as delineated from other scaffoldless techniques in tissue engineering and regenerative medicine. Significantly, during formation, self-organizing and self-assembling tissues display biological processes similar to those that occur in vivo. These processes help lead to the recapitulation of native tissue morphological structure and organization. Notably, functional properties of these engineered tissues, some of which are already in clinical trials, also approach native tissue values. This review endeavors to provide a cohesive summary of work in this field and to highlight the potential of self-organization and the self-assembling process for providing cogent solutions to currently intractable problems in tissue engineering.