In this talk I review a couple of applications on Big Data that I personally like and I try to explain my point of view as a Mathematical Optimizer — especially concerned with discrete (integer) decisions — on the subject. I advocate a tight integration of Machine Learning and Mathematical Optimization (among others) to deal with the challenges of decision-making in Data Science. For such an integration I try to answer three questions: 1) what can optimization do for machine learning? 2) what can machine learning do for optimization? 3) which new applications can be solved by the combination of machine learning and optimization?