For many years the main tools of applied mathematics were restricted to differential equations and theory of dynamical systems. However in the last twenty years we witness an explosion of combinatorial, geometrical and topological ideas applied to very different areas of science. In this talk I will introduce two main working horses of applied topology: persistent homology and mapper algorithm. I will show how they can be obtained from discrete collections of points P and how they can be used to understand the shape of P. The talk will be illustrated with examples of applications of presented tools in very different branches of physical, medical and social sciences. I will also present the main computational challenges and problems in the interface of topology and statistics/machine learning.