The Association Agreements (AAs) and the Deep and Comprehensive Free Trade Areas (DCFTAs) concluded with Ukraine, Moldova and Georgia oblige the EU partner countries to implement in their domestic legal order a significant part of the EU’s acquis, which is annexed to these agreements. However, given that the AAs were negotiated before 2013, the annexed acquis is in most cases outdated because the EU has in the meantime adopted acts that amend, implement, supplement or replace the annexed EU legislation. The AAs foresee procedures to update these annexes to catch up with the relevant legislative developments at EU level. This updating exercise is progressing slowly, but more updates are being prepared. This paper will first analyse the key features of the AAs related to legislative approximation, focussing on the procedures to ‘update’ the annexes (i.e. the procedures that can – or have to – be used to amend the annexed EU legislation to take into account the evolution of EU law). Then, the technical options for broadening the scope of the approximation commitments and market access beyond a mere technical ‘updating’ are explored. This is followed by a chapter-by-chapter overview of the progress of the updating of the AAs and the relevant legislative developments at EU level.