In this talk I shall describe, in survey style, recent results and a number of open problems in the numerical analysis of collocation methods for (systems of) functional-differential and Volterra-type integro-differential equations with variable delays. Part of the talk has been motivated by certain "integral-algebraic" equations arising in, e.g., memory kernel identification problems in heat conduction or in viscoelasticity, or in the mathematical modeling of low-pressure chemical vapor deposition reactors for growing super-conducting films in cellular communications. Since the setting of such IAEs is infinite-dimensional (they may be viewed as abstract DAEs), new approaches for their numerical analysis and computational solution have to be explored. Thus, the current research in this area I am involved in with colleagues at Humboldt University and Virginia Tech encompasses a wide spectrum of mathematics and scientific computation and contains an equally wide range of challenging open problems.