Waste from non-degradable plastics is becoming an increasingly serious problem. Therefore, more and more research focuses on the development of materials with biodegradable properties. Bio-polymers are excellent raw materials for the production of such materials. Bio-based biopolymer films reinforced with nanostructures have become an interesting area of research. Nanocomposite films are a group of materials that mainly consist of bio-based natural (e.g., chitosan, starch) and synthetic (e.g., poly(lactic acid)) polymers and nanofillers (clay, organic, inorganic, or carbon nanostructures), with different properties. The interaction between environmentally friendly biopolymers and nanofillers leads to the improved functionality of nanocomposite materials. Depending on the properties of nanofillers, new or improved properties of nanocomposites can be obtained such as: barrier properties, improved mechanical strength, antimicrobial, and antioxidant properties or thermal stability. This review compiles information about biopolymers used as the matrix for the films with nanofillers as the active agents. Particular emphasis has been placed on the influence of nanofillers on functional properties of biopolymer films and their possible use within the food industry and food packaging systems. The possible applications of those nanocomposite films within other industries (medicine, drug and chemical industry, tissue engineering) is also briefly summarized.