The past three decades have seen the emergence of an endeavor called tissue engineering and regenerative medicine in which scientists, engineers, and physicians apply tools from a variety of fields to construct biological substitutes that can mimic tissues for diagnostic and research purposes and can replace (or help regenerate) diseased and injured tissues. A significant portion of this effort has been translated to actual therapies, especially in the areas of skin replacement and, to a lesser extent, cartilage repair. A good amount of thoughtful work has also yielded prototypes of other tissue substitutes such as nerve conduits, blood vessels, liver, and even heart. Forward movement to clinical product, however, has been slow. Another offshoot of these efforts has been the incorporation of some new exciting technologies (e.g., microfabrication, 3D printing) that may enable future breakthroughs. In this review we highlight the modest beginnings of the field and then describe three application examples that are in various stages of development, ranging from relatively mature (skin) to ongoing proof-of-concept (cartilage) to early stage (liver). We then discuss some of the major issues that limit the development of complex tissues, some of which are fundamentals-based, whereas others stem from the needs of the end users.