Machine Learning (ML) and related "intelligent" computing systems, e.g. search engines, software for image and speech detection and classification, social media filtering devices and recommendation platforms, are widely used in today's society. They belong to an interdisciplinary research area, involving computer science, mathematics, statistics and application domains. Mathematical optimization and related numerical methods are one of the main pillars of this area, providing tools for the computation of the parameters that identify systems aimed at making decisions based on as-yet-unseen data. In this talk, I give a basic overview of optimization methods for ML, from first- to second-order approaches, together with their main properties, pros and cons, and future research directions.