Dynamically driven self-similar measures are an ergodic-theoretic generalization of (homogeneous) self-similar measures. In a 2019 work I proved a general statement on the L^q dimensions of this class of measures on the real line, under a weak exponential separation condition. This result turns out to have a wide variety of applications, including the resolution of Furstenberg's slicing conjecture. I will discuss a generalization of the framework to arbitrary dimension, and an application to a higher rank Furstenberg slicing problem. Joint work with Emilio Corso.