Classical enumerative geometry problems involve counting the number of objects of interest under given constraints. On the other hand, real enumerative geometry problems often involve counting such objects upto signs. In this talk, I will explain enriched version of those frameworks that can be applied to classical, real, and even arithmetic enumerative problems. I will focus on obtaining enriched counts of inflection points (which generalize Weierstrass points) and secant planes of algebraic curves, which are important local invariants of those curves. This talk is based on joint works in progress with Ethan Cotterill, Ignacio Darago, and Naizhen Zhang.