In the industrialized world, cardiovascular disease alone is responsible for almost half of all deaths. Many of the conditions can be treated successfully with surgery, often using transplantation techniques; however, autologous vessels or human-donated organs are in short supply. Tissue engineering aims to create specific, matching grafts by growing cells on appropriate matrices, but there are many steps between the research laboratory and the operating theatre. Neo-tissues must be effective, durable, non-thrombogenic and non-immunogenic. Scaffolds should be bio-compatible, porous (to allow cell/cell communication) and amenable to surgery. In the early days of cardiovascular tissue engineering, autologous or allogenic cells were grown on inert matrices, but patency and thrombogenicity of grafts were disappointing. The current ethos is toward appropriate cell types grown in (most often) a polymeric matrix that degrades at a rate compatible with the cells' production of their own extracellular matrical proteins, thus gradually replacing the graft with a living counterpart. The geometry is crucial. Computer models have been made of valves, and these are used as three-dimensional patterns for mass-production of implant scaffolds. Vessel walls have integral connective tissue architecture, and application of physiological level mechanical forces conditions bio-engineered components to align in precise orientation. This article reviews the concepts involved and successes achieved to date.