The blowup algebra associated with I, in particular the Rees algebra R(I), is an important topic in commutative algebra. For this talk I will be a 2-determinantal ideal, i.e., it is the ideal of maximal minors of a generic 2xn matrix of expected codimension. This includes a range of interesting objects such as rational normal scrolls, certain 2-regular algebraic sets and small schemes. In this talk, I will explain how to determine the degrees of the generators of R(I), the Koszulness of R(I) and the singularities of R(I). This relies crucially on a stratification of the Hilbert scheme of determinantal ideals and the combinatorics of square-free degenerations. This is joint work with Alessio Sammartano.