I will discuss the Attractor Conjecture for Calabi-Yau varieties, which was formulated by Moore in the nineties, highlighting the difference between Calabi-Yau varieties with and without Shimura moduli. In the Shimura case, I show that the conjecture holds and gives rise to an explicit parametrization of CM points on certain Shimura varieties; in the case without Shimura moduli, I'll present counterexamples to the conjecture using unlikely intersection theory. \\ \\ Part of this is joint work with Arnav Tripathy.