The migration of chemical compounds from packaging polymers to food presents a multifaceted challenge with implications for food safety and public health. This review explores the interaction between packaging materials and food products, focusing on permeation, migration, and sorption processes. The different migration mechanisms of contact migration, gas phase migration, penetration migration, set-off migration, and condensation/distillation migration have been discussed comprehensively. The major migrating compounds are plasticizers, nanoparticles, antioxidants, light stabilizers, thermal stabilizers, monomers, oligomers, printing inks, and adhesives, posing potential health risks due to their association with endocrine disruption and carcinogenic effects. Advanced analytical methods help in the monitoring of migrated compounds, facilitating compliance with regulatory standards. Regulatory agencies enforce guidelines to limit migration, prompting the development of barrier coatings and safer packaging alternatives. Furthermore, there is a need to decipher the migration mechanism for mitigating it along with advancements in analytical techniques for monitoring the migration of compounds.