The present review paper focuses on recent developments in edible films and coatings made of base compounds from biological sources, namely plants, animals, algae, and microorganisms. These sources include by-products, residues, and wastes from agro-food industries and sea products that contribute to sustainability concerns. Chitosan, derived from animal biological sources, such as crustacean exoskeletons, has been the most studied base compound over the past three years. Polysaccharides typically constitute no more than 3–5% of the film/coating base solution, with some exceptions, like Arabic gum. Proteins and lipids may be present in higher concentrations, such as zein and beeswax. This review also discusses the enrichment of these bio-based films and coatings with various functional and/or bioactive compounds to confer or enhance their functionalities, such as antimicrobial, antioxidant, and anti-enzymatic properties, as well as physical properties. Whenever possible, a comparative analysis among different formulations was performed. The results of the applications of these edible films and coatings to fruit and vegetable products are also described, including shelf life extension, inhibition of microbial growth, and prevention of oxidation. This review also explores novel types of packaging, such as active and intelligent packaging. The potential health benefits of edible films and coatings, as well as the biodegradability of films, are also discussed. Finally, this review addresses recent innovations in the edible films and coatings industry, including the use of nanotechnologies, aerogels, and probiotics, and provides future perspectives and the challenges that the sector is facing.