It is estimated that the number of patients requiring heart valve replacement will triple over the next five decades. None of the current replacement valves can fully restore native valve function because they lack growth and remodeling capabilities. Heart valve tissue engineering is a promising technology to overcome these limitations. Various approaches are being employed, either aimed at development of the valve substitute in vitro or at the use of the regenerative potential of the body (in situ) for the tissue culture phase. This review provides an overview of the progress within both the in vitro and in situ tissue engineering approaches for trileaflet heart valve tissue engineering. Current challenges with these approaches are discussed, focusing in particular on the use of synthetic scaffold materials.