The development of packaging technology has become a crucial part of the food industry in today’s modern societies, which are characterized by technological advancements, industrialization, densely populated cities, and scientific advancements that have increased food production over the past 50 years despite the lack of agricultural land. Various types of food-packaging materials are utilized, with plastic being the most versatile. However, there are certain concerns with regards to the usage of plastic packaging because of unreacted monomers’ potential migration from the polymer packaging to the food. The magnitude of monomer migration depends on numerous aspects, including the monomer chemistry, type of plastic packaging, physical–chemical parameters such as the temperature and pH, and food chemistry. The major concern for the presence of packaging monomers in food is that some monomers are endocrine-disrupting compounds (EDCs) with a capability to interfere with the functioning of vital hormonal systems in the human body. For this reason, different countries have resolved to enforce guidelines and regulations for packaging monomers in food. Additionally, many countries have introduced migration testing procedures and safe limits for packaging monomer migration into food. However, to date, several research studies have reported levels of monomer migration above the set migration limits due to leaching from the food-packaging materials into the food. This raises concerns regarding possible health effects on consumers. This paper provides a critical review on plastic food-contact materials' monomer migration, including that from biodegradable plastic packaging, the monomer migration mechanisms, the monomer migration chemistry, the key factors that affect the migration process, and the associated potential EDC human health risks linked to monomers' presence in food. The aim is to contribute to the existing knowledge and understanding of plastic food-packaging monomer migration.