Abstract: Silicon/silicon-germanium heterostructures have many important advantages for hosting spin qubits. However, controlling the energy splitting between the two low-energy conduction-band valley states remains a critical challenge for scaling up to large numbers of reliable and reproducible qubits. Broad distributions of valley splittings are commonplace, even among quantum dots on the same device. Such behavior has previously been attributed to imperfections such as steps at the quantum well interface, which are known to strongly suppress the valley splitting. Many heterostructure designs have been proposed to boost the valley splitting, to overcome this problem. In this talk, we explore a simple, universal theory of valley splitting based on the reciprocal-space profile of the quantum-well confinement potential, which can explain the effects of steps, wide interfaces, alloy disorder, and custom heterostructure designs. We use this understanding to theoretically characterize the valley splitting in a variety of heterostructures, finding that alloy disorder causes substantial variations of the valley splitting, even in the absence of steps. Using this understanding, we lay out two approaches to engineer large valley splittings: one based on deterministically increasing the Fourier component of the quantum well potential that couples the valleys, and one that takes advantage of disorder to statistically increase the valley splitting.