The investigation of new photosensitizers for Grätzel-type organic dye-sensitized solar cells (DSSCs) remains a topic of interest for researchers of alternative solar cell materials. Over the past 20 years, considerable and increasing research efforts have been devoted to the design and synthesis of new materials, based on “donor, π-conjugated bridge, acceptor” (D–π–A) organic dye photosensitizers. In this paper, the computational chemistry methods are outlined and the design of organic sensitizers (compounds, dyes) is discussed. With reference to recent literature reports, rational molecular design is demonstrated as an effective process to study structure–property relationships. Examples from established organic dye sensitizer structures, such as TA-St-CA, Carbz-PAHTDDT (S9), and metalloporphyrin (PZn-EDOT), are used as reference structures for an examination of this concept applied to generate systematically modified structural derivatives and hence new photosensitizers (i.e., dyes). Using computer-aided rational design (CARD), the in silico design of new chromophores targeted an improvement in spectral properties via the tuning of electronic structures by substitution of molecular fragments, as evaluated by the calculation of absorption profiles. This mini review provides important rational design strategies for engineering new organic light-absorbing compounds towards improved spectral absorption and related optoelectronic properties of chromophores for photovoltaic applications, including the dye-sensitized solar cell (DSSC).