Environmental pollution by synthetic polymers is a global problem and investigating substitutes for synthetic polymers is a major research area. Starch can be used in formulating bioplastic materials, mainly as blends or composites with other polymers. The major drawbacks of using starch in such applications are water sensitivity and poor mechanical properties. Attempts have been made to improve the mechanical properties of starch-based blends and composites, by e.g., starch modification or plasticization, matrix reinforcement, and polymer blending. Polymer blending can bring synergetic benefits to blends and composites, but necessary precautions must be taken to ensure the compatibility of hydrophobic polymers and hydrophilic starch. Genetic engineering offers new possibilities to modify starch inplanta in a manner favorable for bioplastics applications, while the incorporation of antibacterial and/or antioxidant agents into starch-based food packaging materials brings additional advantages. In conclusion, starch is a promising material for bioplastic production, with great potential for further improvements. This review summarizes the recent advances in starch-based blends and composites and highlights the potential strategies for overcoming the major drawbacks of using starch in bioplastics applications.