In mathematics, homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of interrelated (sometimes surprisingly so) conjectures relating various homological properties of a commutative ring to its internal ring structure, particularly its Krull dimension and depth.

The following list given by Melvin Hochster is considered definitive for this area. In the sequel, ${\displaystyle A,R}$, and ${\displaystyle S}$ refer to Noetherian commutative rings; ${\displaystyle R}$ will be a local ring with maximal ideal ${\displaystyle m_{R}}$, and ${\displaystyle M}$ and ${\displaystyle N}$ are finitely generated ${\displaystyle R}$-modules.