Machine learning is gaining more popularity among applied mathematicians as a valuable tool. This talk aims to provide an overview of the capability of this important tool and a roadmap for mastering it. I will begin with an overview of machine learning's roles in mathematical modelling, including its ability to provide highly flexible approximation models and methods for solving mathematical models. Next, I will introduce the general approach and concepts of machine learning by drawing connections to classical mathematical concepts such as approximation and interpolation/extrapolation. Much emphasis will be given to the revolutionary sub-field of deep learning. Lastly, I will cover several important applications of machine learning in mathematical modeling, including multiphysics problems, fluid modelling, inverse problems, combinatorial optimization problems, time series modelling.