Starting from the original formulation of a spectral curve (which provides the initial data for topological recursion) of Eynard and Oratin in 2007, we will discuss the more recent notions of admissibility conditions for spectral curves and (in)effective ramification points. The latter gives a precise criteria for when one can omit a ramification point in the recursion formula, while the former are conditions on the spectral curve that need to hold for TR to be well-defined. These were derived using the formalism of Airy structures, an algebraic generalization of topological recursion. Part of the talk is closely based upon a recent work by Belliard-Bouchard-Kramer-Nelson arXiv:2412.09120.