An account is made of the experimental, theoretical, and computational developments that led to our current understanding of the colloidal aggregation problem when a gravitational field is present. Starting with unaggregated colloids, a review is made of the advances that led to the founding of the barometric equation for the distribution of colloidal particles in a suspension, noticing that for large bodies, like large colloidal aggregates, their final fate in equilibrium is to be at the bottom of the container. Then, we briefly review the aggregation of colloids in the absence of gravity that has been amply studied by both experiments and simulations. For this purpose, the paradigmatic case of the DLVO interaction is taken as an example. Next, a brief revision is made of the seminal experimental work of C. Allain and collaborators on the colloidal aggregation problem when an external gravitational field is present, centering our study in the nongelling situations, that is, for dilute colloidal suspensions, when only sedimentation and deposition of single clusters occur. Afterward, the development of different computer simulations that treat this case of single cluster sedimentation and deposition is reviewed, and note how the different improvements of the algorithms lead to better correspondences with the experimental systems. We finally discuss further possible improvements of the algorithms and end with proposals for future work
