Introduced by C.C. Chang in the 1950s, MV algebras are to many-valued (Lukasiewicz) logics what boolean algebras are to two-valued logic. On the other hand, effect algebras are a class of partial algebras recently introduced by mathematical physicists to describe quantum effects. We first discuss how these two structures are intimately related in the sense that there is a non-full subcategory of effect algebras isomorphic to the category of MV algebras, and look at the construction of coequalizers for effect algebras (by Bart Jacobs) - a task made difficult by the partiality - and use this to characterize the regular monomorphisms. In the second half of the talk, we discuss coordinatization of MV algebras (Lawson \& Scott, and also Wehrung) - i.e. MV algebras can be realized as the lattice of principal ideals of boolean inverse semigroups. We give an example of the coordinatization of the rationals in $[0,1]$ and present a decomposition theorem that generalizes the approach taken, which may be useful for future concrete coordinatization examples.