  The design of novel protein sequences with targeted functionalities underpins
a central theme in protein engineering, impacting diverse fields such as drug
discovery and enzymatic engineering. However, navigating this vast
combinatorial search space remains a severe challenge due to time and financial
constraints. This scenario is rapidly evolving as the transformative
advancements in AI, particularly in the realm of generative models and
optimization algorithms, have been propelling the protein design field towards
an unprecedented revolution. In this survey, we systematically review recent
advances in generative AI for controllable protein sequence design. To set the
stage, we first outline the foundational tasks in protein sequence design in
terms of the constraints involved and present key generative models and
optimization algorithms. We then offer in-depth reviews of each design task and
discuss the pertinent applications. Finally, we identify the unresolved
challenges and highlight research opportunities that merit deeper exploration.
