Plastic production has outgrown most other man-made materials, with more than 90% being petroleum-based and nonbiodegradable. Packaging, primarily food packaging, consumes the most plastic and is the largest contributor to municipal solid waste. In addition, its dependence on crude oil feedstock makes the plastic industry unsustainable and renders plastic markets vulnerable to oil price volatility. Therefore, the development of bioalternatives to conventional plastics is now a priority of the food packaging industry. Bioplastics are polymers that are either biobased (fully or partially), or biodegradable, or both. This review aims to provide an insightful overview of the most recent research and development successes in bioplastic materials, focusing on food packaging applications. Bioplastics are compared to their conventional counterparts with respect to their mechanical, thermal, barrier, and processability properties. The gaps between bio- and conventional plastics in food packaging are elucidated. Potential avenues for improving bioplastic properties to broaden their food packaging applications are critically examined. Furthermore, two of the most controversial topics on bioplastic alternatives, sustainability assessment and their impact on the plastic waste management system, are discussed.