Having just listened to some of Jacob Tsimerman's <a href="https://www.math.princeton.edu/events/seminars/minerva-mini-course/archive/240">Minerva lectures</a>, I became aware of the recent arXiv preprint, <a href="https://arxiv.org/abs/2109.08788">Canonical Heights on Shimura Varieties and the André&ndash;Oort Conjecture</a>, by Jonathan Pila, Ananth N. Shankar, Jacob Tsimerman, Hélène Esnault, and Michael Groechenig.  Assuming the paper is correct, it gives the first unconditional (i.e., not assuming the Generalized Riemann Hypothesis) proof of the full <a href="https://en.wikipedia.org/wiki/Andr%C3%A9%E2%80%93Oort_conjecture">André&ndash;Oort Conjecture</a>.  The proof builds on a lot of previous work and knits together a wide variety of techniques and ideas, but one thing that I find personally appealing is that the theory of <a href="https://en.wikipedia.org/wiki/O-minimal_theory">o-minimality</a> plays a key role behind the scenes.  A priori, one might not guess that model theory has much to say about counting rational points, but it does!