First I will give a survey about regularity properties of sets of reals, the relationship to forcing notions on the reals, and to cardinal characteristics of the continuum (Cichon’s Diagram). I will present a general framework which is useful in this research area, based on Zapletal’s theory of “Idealized Forcing”. Then I will present some results concerning higher levels of the projective hierarchy, based on my work with Vera Fischer and Sy Friedman from 2014.