Vital research has been carried out on the sustainable organic fraction of municipal solid waste (OFMSW) stream management in the last five years. In addition to the traditional approach to reducing its environmental side effects, considering OFMSW as a feedstock to produce bioproducts, such as enzymes, bioplastics, biopesticides, and other high-value products, represents a key component in the transformation of OFMSW treatment plants (biogas or mechanical–biological treatment (MBT) plants) into biorefineries. This short review is intended to assess and analyze the current state of knowledge of OFMSW treatment technologies, suggest practical solution options, and identify future research and development needs to help promote more sustainable management of this underutilized and ever-growing waste stream.