Let $K$ be a number field. Beginning in the 1970s, Mazur's "Program B" kicked off efforts to classify the $K$-rational points on all modular curves $X_H$, as $H$ ranges through open subgroups of $\text{GL}_2(\hat{\mathbb Z})$. Fifty years later, it remains a very active field of research in arithmetic geometry: even as late as 2017, the determination of the rational points on a single "cursed curve" was heralded a breakthrough in the subject. In this talk, we will outline a possible approach to settle Mazur's Program B completely. The inputs required are (1) a resolution to Serre's uniformity question in full generality, and (2) an algorithm to obtain rational points on any modular curve of genus at least 2. For (1), we discuss a possible approach via Borcherds products, and for (2), we discuss equationless approaches to quadratic and motivic Chabauty algorithms, following the respective recent work of Balakrishnan-Dogra-Muller-Tuitman-Vonk and Corwin.