Dye aggregation dictates structural and optoelectronic properties of photoelectrodes in dye-sensitized solar cells (DSSCs), thereby playing an essential role in their photovoltaic performance. It is therefore important to understand this molecular phenomenon so that dye aggregation can be suitably controlled in DSSC devices. Accordingly, this review presents the molecular origins of dye aggregation, manifestations of hypsochromic (H) and bathochromic (J) dye aggregation in DSSCs, a classification of the molecular factors that cause this aggregation, and ways by which dye aggregation can be suppressed in cases where it is undesirable. To this end, a classification of molecular engineering methods that are being used in order to better understand and control dye aggregation is described. The review concludes with a broader outlook on how molecular aggregation in chromophores can similarly effect a wider range of optoelectronic phenomena.