Bioplastics, which are plastic materials produced from renewable bio-based feedstocks, have been investigated for their potential as an attractive alternative to petroleum-based plastics. Despite the harmful effects of plastic accumulation in the environment, bioplastic production is still underdeveloped. Recent advances in strain development, genome sequencing, and editing technologies have accelerated research efforts toward bioplastic production and helped to advance its goal of replacing conventional plastics. In this review, we highlight bioengineering approaches, new advancements, and related challenges in the bioproduction and biodegradation of plastics. We cover different types of polymers, including polylactic acid (PLA) and polyhydroxyalkanoates (PHAs and PHBs) produced by bacterial, microalgal, and plant species naturally as well as through genetic engineering. Moreover, we provide detailed information on pathways that produce PHAs and PHBs in bacteria. Lastly, we present the prospect of using large-scale genome engineering to enhance strains and develop microalgae as a sustainable production platform.