We will survey a few results on modular curves that arise from Serre's open image theorem for elliptic curves over the rationals. Mazur's Program B loosely asks for a complete classification of the possible images in Serre's theorem. We will discuss how close/far we are from addressing Program B over the rationals and we will highlight a finite number of modular curves whose rational points should be further studied. We also consider quadratic points over modular curves.