The formation of aggregates in protein-based pharmaceuticals is a major issue that can compromise drug safety and drug efficacy. With a view to improving protein stability, considerable effort is put forth to unravel the fundamental mechanisms underlying the aggregation process. However, therapeutic protein aggregation is a complex multistep phenomenon that involves time and length scales spanning several orders of magnitude, and strategies addressing protein aggregation inhibition are currently still largely empirical in practice. Here, we review how key concepts developed in the frame of colloid science can be applied to gain knowledge on the kinetics and thermodynamics of therapeutic protein aggregation across different length scales. In particular, we discuss the use of coarse-grained molecular interaction potentials to quantify protein colloidal stability. We then show how population balance equations simulations can provide insights into the mechanisms of aggregate formation at the mesoscale, and we highlight the strength of the concept of fractal scaling to quantify irregular aggregate morphologies. Finally, we correlate the macroscopic rheological properties of protein solutions with the occupied volume fraction and the aggregate structure. Overall, this work illustrates the power and limitations of colloidal approaches in the multiscale description of the aggregation of therapeutic proteins.