  Consider a complex algebraic group $G$ acting on a smooth variety $M$ with
finitely many orbits, and let $\Omega$ be an orbit. The following three
invariants of $\Omega\subset M$ can be characterized axiomatically: (1) the
equivariant fundamental class $[\overline{\Omega}, M]\in H^*_G(M)$, (2) the
equivariant Chern-Schwartz-MacPherson class $c(\Omega, M)\in H^*_G(M)$, and (3)
the equivariant motivic Chern class $mC(\Omega, M) \in K_G(M)[y]$. The axioms
for Chern-Schwartz-MacPherson and motivic Chern classes are motivated by the
axioms for cohomological and K-theoretic stable envelopes of Okounkov and his
coauthors. For $M$ a flag variety and $\Omega$ a Schubert cell---an orbit of
the Borel group acting---this implies that CSM and MC classes coincide with the
weight functions studied by Rimanyi-Tarasov-Varchenko. In this paper we review
the general theory and illustrate it with examples.
