Organic photovoltaic (OPV) devices, made with semiconducting polymers, have recently attained a power conversion efficiency (PCE) over 14% in single junction cells and over 17% in tandem cells. These high performances, together with the suitability of the technology to inexpensive large-scale manufacture, over lightweight and flexible plastic substrates using roll-to-roll (R2R) processing, place the technology amongst the most promising for future harvesting of solar energy. Although OPVs using non-fullerene acceptors have recently outperformed their fullerene-based counterparts, the research in the development of new fullerenes and in the improvement of the bulk-heterojunction (BHJ) morphology and device efficiency of polymer:fullerene solar cells remains very active. In this review article, the most relevant research works performed over the last 3 years, that is, since the year 2016 onwards, in the field of fullerene-based polymer solar cells based on the copolymers PTB7, PTB7-Th (also known as PBDTTT-EFT) and PffBT4T-2OD, are presented and discussed. This review is primarily focused on studies that involve the improvement of the BHJ morphology, efficiency and stability of small active area devices (typically < 15 mm2), through the use of different processing strategies such as the use of different fullerene acceptors, different processing solvents and additives and different thermal treatments.