Poly(lactic acid) (PLA) is the most widely produced biobased, biodegradable and biocompatible polyester. Despite many of its properties are similar to those of common petroleum-based polymers, some drawbacks limit its utilization, especially high brittleness and low toughness. To overcome these problems and improve the ductility and the impact resistance, PLA is often blended with other biobased and biodegradable polymers. For this purpose, poly(butylene adipate-co-butylene terephthalate) (PBAT) and poly(butylene succinate-co-butylene adipate) (PBSA) are very advantageous copolymers, because their toughness and elongation at break are complementary to those of PLA. Similar to PLA, both these copolymers are biodegradable and can be produced from annual renewable resources. This literature review aims to collect results on the mechanical, thermal and morphological properties of PLA/PBAT and PLA/PBSA blends, as binary blends with and without addition of coupling agents. The effect of different compatibilizers on the PLA/PBAT and PLA/PBSA blends properties is here elucidated, to highlight how the PLA toughness and ductility can be improved and tuned by using appropriate additives. In addition, the incorporation of solid nanoparticles to the PLA/PBAT and PLA/PBSA blends is discussed in detail, to demonstrate how the nanofillers can act as morphology stabilizers, and so improve the properties of these PLA-based formulations, especially mechanical performance, thermal stability and gas/vapor barrier properties. Key points about the biodegradation of the blends and the nanocomposites are presented, together with current applications of these novel green materials.