R: commutative Artin ring,

In the representation theory of Artin algebras there is a well-known conjecture: Given an arbitrary Artin algebra, its finitistic dimension is finite. This is called the finitistic dimension conjec-ture. It is over 45 years old and remains open to date. In this note, we survey its developments, and report some of the new advances on the finitistic dimension conjecture. 1 1. The conjectur