The author presents a survey of recent results on the attainable order of (super-)convergence of collocation solutions for systems of Volterra functional integro-differential equations of the form
Here, is a delay function, and the (nonlinear) operator is either the Nemytskij operator (or: substitution operator) with delay, , , or the weakly singular delay Volterra integral operator ,
with kernel given by
While the right-hand side in (1) could also depend on more general (non-Hammerstein) operators, including delay operators, the author restricts the analysis to Volterra integral operators of the form . The functions , , , and are assumed to be smooth on their respective domains. Related functional equations and theoretical and computational aspects of collocation methods for their solution are described.