  Allocating resources to individuals in a fair manner has been a topic of
interest since ancient times, with most of the early mathematical work on the
problem focusing on resources that are infinitely divisible. Over the last
decade, there has been a surge of papers studying computational questions
regarding the indivisible case, for which exact fairness notions such as
envy-freeness and proportionality are hard to satisfy. One main theme in the
recent research agenda is to investigate the extent to which their relaxations,
like maximin share fairness (MMS) and envy-freeness up to any good (EFX), can
be achieved. In this survey, we present a comprehensive review of the recent
progress made in the related literature by highlighting different ways to relax
fairness notions, common algorithm design techniques, and the most interesting
questions for future research.
