Professor T.C. Papanastasiou's contributions to rheology and computational fluid mechanics are numerous and have a lasting effect. In the short span of a professional career of about 10 years, and in such diverse places as the University of Minnesota, the University of Michigan, and the Aristotle University of Thessaloniki, he developed and implemented new ideas in the fields of rheology and computational fluid mechanics. He dealt with such important topics as: i) modelling of viscoelasticity and viscoplasticity through appropriate constitutive equations; ii) numerical techniques based on the finite element method, streamline integration, inverse of the unknown, and Newton iteration for integral-differential equations; iii) numerical simulation of important polymer processes, such as fiber spinning, film blowing, film casting, extrusion and coextrusion of polymeric liquids; iv) stability analysis of multiple flows; v) three-dimensional computational techniques for generalized Newtonian flows; vi) numerical analysis of viscoplastic flows; vii) solidification problems; viii) outflow boundary conditions, etc. His many contributions include authoring two books in the area of fluid mechanics, one for undergraduate and the other for graduate use. He was a mentor and an advisor to a dozen people, his former students, who have, in their own right, successful careers, some as professors, others as research engineers in major industries. The ideas and foundations of his work are currently pursued and studied by many researchers world-wide, and in this manner it is the most appropriate tribute to him and a guarantee that his name will be remembered for years to come.