Regenerative medicine holds much promise in assisting patients to recover from injured or lost tissues and organs through organism reconstruction. Three-dimensional (3D) biomimetic models via various approaches can be used by pharmaceutical industry for controlled drug delivery. With proper biomaterials and engineering technologies, drugs can be released in a rate-manipulated manner towards targeted regions with spatial and temporal effects. Much of the success is a result of a combination of growth factors, stem cells, biomaterials, nanotechnologies, electrospinning and 3D printing techniques mimicking in vivo angiogenesis, histogenesis and tumorigenesis processes. This interdisciplinary field on biomimetic drug delivery and regenerative medicine has already opened up a new avenue for medical progress and reformation. This article presents a comprehensive review of the 3D biomimetic models in the pertinent fields of tissue and organ manufacturing, cell-material mutual interactions, bioactive agent carrier systems and anti-cancer drug delivery methods. Particularly, the potential trends and challenges of tissue and organ manufacturing are discussed from different perspectives.