The current development of science and the contemporary market, combined with high demands from consumers, force manufacturers and scientists to implement new solutions in various industries, including the packaging industry. The emergence of new solutions in the field of intelligent packaging has provided an opportunity to extend the quality of food products and ensures that food will not cause any harm to the consumer’s health. Due to physical, chemical, or biological factors, the state of food may be subject to degradation. The degradation may occur because the packaging, i.e., the protective element of food products, may be damaged during storage, transport, or other logistic and sales activities. This is especially important since most food products are highly perishable, and the maintenance of the quality of a food product is the most critical issue in the entire supply chain. Given the importance of the topic, the main purpose of this article was to provide a general overview of the application of biosensors, sensors, and tags in intelligent packaging used for food products. A short history and the genesis of intelligent packaging are presented, and the individual possibilities of application of sensors, biosensors, gas sensors, and RFID tags, as well as nanotechnology, in the area of the packaging of food products are characterized.