  This is a brief overview of work done by Ian Anderson, Mark Fels, and myself
on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject
closely related to Palais' Principle of Symmetric Criticality. After providing
a little history, I describe necessary and sufficient conditions on a group
action such that reduction of a group-invariant Lagrangian by the symmetry
group yields the correct symmetry-reduced Euler-Lagrange equations.
