Models on drying of durum wheat pasta and enriched pasta were reviewed to identify avenues for improvement according to consumer needs, product formulation and processing conditions. This review first summarized the fundamental phenomena of pasta drying, mass transfer, heat transfer, momentum, chemical changes, shrinkage and crack formation. The basic equations of the current models were then presented, along with methods for the estimation of pasta transport and thermodynamic properties. The experimental validation of these models was also presented and highlighted the need for further model validation for drying at high temperatures (>−100°C) and for more accurate estimation of the pasta diffusion and mass transfer coefficients. This review indicates the need for the development of mechanistic models to improve our understanding of the mass and heat transfer mechanisms involved in pasta drying, and to consider the local changes in pasta transport properties and relaxation time for more accurate description of the moisture transport near glass transition conditions. The ability of current models to describe dried pasta quality according to the consumers expectations or to predict the impact of incorporating ingredients high in nutritional value on the drying of these enriched pasta was also discussed.