  This is a survey on recent developments on unimodality, log-concavity and
real-rootedness in combinatorics. Stanley and Brenti have written extensive
surveys of various techniques that can be used to prove real-rootedness,
log-concavity or unimodality. After a brief introduction, we will complement
these surveys with a survey over some new techniques that have been developed,
as well as problems and conjectures that have been solved. This is a draft of a
chapter to appear in Handbook of Enumerative Combinatorics, published by CRC
Press.
