(Based on joint work with Yang Li). I will present an overview of Donaldson’s program to extend the methods of gauge theory and Floer homology from 3- and 4-manifolds to higher dimensions, with a focus in this talk on Calabi-Yau 3-folds. After discussing the background material in gauge theory and Calabi-Yau geometry, I will highlight the main challenge in pursuing this program: the non-compactness problems. I will then mention three related key conjectures and outline our joint works with Yang Li to resolve them: (1) proof of the local Donaldson-Scaduto conjecture on the existence of pair-of-pants special Lagrangians, (2) progress on the Donaldson-Segal conjecture, including a compactness theorem for monopole Fueter sections on 3-manifolds, and if time permits, (3) a proposal for a hyperkähler Atiyah-Floer conjecture.