Instantons in string theory can generate superpotential corrections useful for moduli stabilization or the existence of phenomenologically relevant couplings. In this talk, I will consider these issues from three points of view. First, I will present systematic "bottom-up" work on a class of MSSM-like gauge theories with anomalous U(1)'s (from IIa intersecting branes, e.g.). I will briefly discuss the importance of instantons for couplings in these theories. Instead the focus will mostly be on constraints on chiral matter necessary for string consistency, including the structure of matter beyond the MSSM "preferred" by these constraints. Next, I will discuss the computation and physics of instanton corrections in F-theory. Utilizing heterotic / F-theory duality, I will draw general conclusions about the moduli-dependent (Pfaffian) prefactor, including connections to the 7-brane gauge theory, and will also discuss some explicit examples. Finally, if time permits, I will briefly discuss how the systematic consideration of instanton effects leads one to the study of diophantine equations and will generalize the importance of diophantines to any physical effect defining a recursive set. I will argue that this gives rise to an issue of computability in the landscape by relation to Hilbert's tenth problem.