This review article covers the synthesis and design of conjugated polymers for carefully adjusting energy levels and energy band gap (EBG) to achieve the desired photovoltaic performance. The formation of bonds and the delocalization of electrons over conjugated chains are both explained by the molecular orbital theory (MOT). The intrinsic characteristics that classify conjugated polymers as semiconducting materials come from the EBG of organic molecules. A quinoid mesomeric structure (D-A ↔ D+ = A-) forms across the major backbones of the polymer as a result of alternating donor-acceptor segments contributing to the pull-push driving force between neighboring units, resulting in a smaller optical EBG. Furthermore, one of the most crucial factors in achieving excellent performance of the polymer is improving the morphology of the active layer. In order to improve exciton diffusion, dissociation, and charge transport, the nanoscale morphology ensures nanometer phase separation between donor and acceptor components in the active layer. It was demonstrated that because of the exciton's short lifetime, only small diffusion distances (10-20 nm) are needed for all photo-generated excitons to reach the interfacial region where they can separate into free charge carriers. There is a comprehensive explanation of the architecture of organic solar cells using single layer, bilayer, and bulk heterojunction (BHJ) devices. The short circuit current density (Jsc), open circuit voltage (Voc), and fill factor (FF) all have a significant impact on the performance of organic solar cells (OSCs). Since the BHJ concept was first proposed, significant advancement and quick configuration development of these devices have been accomplished. Due to their ability to combine great optical and electronic properties with strong thermal and chemical stability, conjugated polymers are unique semiconducting materials that are used in a wide range of applications. According to the fundamental operating theories of OSCs, unlike inorganic semiconductors such as silicon solar cells, organic photovoltaic devices are unable to produce free carrier charges (holes and electrons). To overcome the Coulombic attraction and separate the excitons into free charges in the interfacial region, organic semiconductors require an additional thermodynamic driving force. From the molecular engineering of conjugated polymers, it was discovered that the most crucial obstacles to achieving the most desirable properties are the design and synthesis of conjugated polymers toward optimal p-type materials. Along with plastic solar cells (PSCs), these materials have extended to a number of different applications such as light-emitting diodes (LEDs) and field-effect transistors (FETs). Additionally, the topics of fluorene and carbazole as donor units in conjugated polymers are covered. The Stille, Suzuki, and Sonogashira coupling reactions widely used to synthesize alternating D-A copolymers are also presented. Moreover, conjugated polymers based on anthracene that can be used in solar cells are covered.