Abstract: The study of stochastic Volterra equations with non-Lipschitz continuous coefficients has recently attracted quite some attention, motivated by their very successful applications as well-suited volatility models in mathematical finance. While stochastic Volterra equations with Lipschitz continuous coefficients are well-studied integral equations, in the case of less regular coefficients many fundamental questions are still open. In this talk we discuss the existence of strong and weak solutions as well as pathwise uniqueness of stochastic Volterra equations with time-inhomogeneous non-Lipschitz continuous coefficients. Moreover, we introduce neural stochastic Volterra equations as a physics-inspired architecture, generalizing the class of neural stochastic differential equations, and investigate supervised learning problems for time evolutions of random systems with memory effects and irregular behaviour. The talk is based on joint work with David Scheffels.