We review the theoretical framework underlying the description of transverse single-spin asymmetries (SSAs) for both collinear and transverse-momentum-dependent (TMD) processes. For the latter, we discuss modifications to the widely used CSS formalism that are needed to address certain issues that have arisen in TMD analyses. After these improvements, one can derive rigorous relations between collinear and TMD functions. Moreover, we show how both collinear and TMD SSA observables are driven by multi-parton correlations, which allows for a future global extraction to be performed including data from both types of measurements.