Research toward bio-based and biodegradable polymers has received a lot of attention these last years, due to environmental concerns and the need to replace fossil resources. Starch is in this frame an interesting starting material due to its abundance and low cost. Native starch displays however, poor mechanical properties and is highly hydrophilic. New starch-based thermoplastic materials can be prepared to overcome these drawbacks by chemical modification, and notably graft copolymerization. A large range of polymers can be grafted on starch by ring-opening and radical polymerizations of various monomers in order to modulate the properties of the final product. Polymers can also be directly grafted onto starch using coupling strategies. This review presents the state of the art in the field.