In this talk, I will present some of my recent work on the dynamical systems in machine learning. This includes a mean-field optimal control approach to the training of NeurODEs, where we consider a measure-theoretical formulation of the training of NeurODEs in the form of a mean-field optimal control problem. Then we propose an alternative way to train Neuro Networks by using the first-order optimality conditions, which will take the form of the Pontryagin Maximum Principle (PMP). I will also talk about interacting particle systems used in the optimization methods of Metaheuristics, such as Particle Swarm Optimization (PSO) and Consensus-Based Optimization (CBO), where particles explore the landscape of the pay-off function one wishes to minimize until they reach a consensus at one of the global minimizers. Especially, we will focus on a CBO method for constraint problems on the sphere, which has applications in machine learning problems like Principle Component Analysis (PCA).