Food packaging has a crucial function in the modern food industry. New food packaging technologies seek to meet consumers and industrial's demands. Changes related to food production, sale practices and consumers' lifestyles, along with environmental awareness and the advance in new areas of knowledge (such as nanotechnology or biotechnology), act as driving forces to develop smart packages that can extend food shelf-life, keeping and supervising their innocuousness and quality and also taking care of the environment. This review describes the main concepts and types of active and intelligent food packaging, focusing on recent progress and new trends using biodegradable and biobased polymers. Numerous studies show the great possibilities of these materials. Future research needs to focus on some important aspects such as possibilities to scale-up, costs, regulatory aspects, and consumers' acceptance, to make these systems commercially viable.