The excellent collection ability of the photo-generated holes from the poly-crystalline lead trihalide perovskite thin films to the poly[3-(4-carboxybutyl)thiophene-2,5,-diyl] (P3CT) or poly(3-hexylthiophene) (P3HT) polymer layer has been used to realize the highly efficient solar cells. The electronic and molecular structures of the p-type polymers play the decisive roles in the photovoltaic responses of the resultant perovskite solar cells. It is fundamental to understand the relation between the material properties and the photovoltaic performance in order to achieve the highest power conversion efficiency. We review the molecular packing, morphological, optical, excitonic, and surface properties of the P3CT and P3HT polymer layers in order to correctly understand the working mechanisms of the resultant solar cells, thereby predicting the required material properties of the used p-type polymers as the efficient hole transport layer (HTL).