Solar cells (SCs) are of considerable current research interest because of their potential as a clean alternative to fossil fuels. Researchers across the globe are developing novel polymeric materials with enhanced power conversion efficiency (PCE). Conjugated poly-ynes and poly(metalla-ynes) incorporating late transition metals and thiophene-based spacers have played a very important role in this strategic area of materials research. The performance of the SCs can be optimized by varying the conjugated spacers and/or the metal ions along the polymer backbone. Therefore, an analysis of structure-photovoltaic property relationships in poly-ynes and poly(metalla-ynes) is desirable as a guide for the development of new functional materials for use in SCs. Keeping the importance of this strategic topic in mind, herein we present a brief review on conjugated poly-ynes and poly(metalla-ynes) incorporating thiophene-based spacers that have potential SC applications. Attempts have been made to correlate the photovoltaic performance of the SCs to the chemical structure of thiophene-incorporated poly-ynes and poly(metalla-ynes). The performance of SCs is also strongly influenced by other factors such as morphology and device structure.