Population growth and the rising enthusiasm for meat consumption in developing countries have increased the global demand for animal protein. The limited increase in traditional meat production, which results in high resource consumption, greenhouse gas emissions, and zoonotic diseases, has affected the sustainable supply of meat protein. The technological development and commercialization of meat analogs derived from plant and microbial proteins provide a strategy for solving the abovementioned problems. However, before these innovative foods are marketed, they should comply with regulations and standards to ensure food safety and consumer rights. This review briefly summarizes the global development status and challenges of plant- and fungi-based meat analog products. It focuses on the current status, characteristics, and disputes in the regulations and standards worldwide for plant- and fungi-based meat analogs and proposes suggestions for perfecting the regulatory system from the perspective of ensuring safety and supporting innovation. Although plant- and fungi-based meat analogs have had a history of safe usage as foods for a certain period around the world, the nomenclature and product standards are uncertain, which affects product innovation and global sales. Regulatory authorities should promptly formulate and revise regulations or standards to clarify the naming of meat analogs and product standards, especially the use of animal-derived ingredients and limits of nutrients (e.g., protein, fat, vitamins, and minerals) to continuously introduce start-up products to the market.