  We consider Artinian algebras $A$ over a field $\mathsf{k}$, both graded and
local algebras. The Lefschetz properties of graded Artinian algebras have been
long studied, but more recently the Jordan type invariant of a pair $(\ell,A)$
where $\ell$ is an element of the maximal ideal of $A$, has been introduced.
The Jordan type gives the sizes of the Jordan blocks for multiplication by
$\ell$ on $A$, and it is a finer invariant than the pair $(\ell,A)$ being
strong or weak Lefschetz. The Jordan degree type for a graded Artinian algebra
adds to the Jordan type the initial degree of ``strings'' in the decomposition
of $A$ as a $\mathsf{k}[\ell]$ module. We here give a brief survey of Jordan
type for Artinian algebras, Jordan degree type for graded Artinian algebras,
and related invariants for local Artinian algebras, with a focus on recent work
and open problems.
