The Opening Conference and Boot Camp of the Thematic Program on Statistical Inference, Learning, and Models for Big Data was held at the Fields Institute in Toronto from January 12th to January 23rd, 2015. A total of 35 scientific talks were presented, providing an overview of the main themes of the Program. Even if big data problems from numerous fields were covered, common challenges emerged and some tools were seen in many different contexts. A number of successful applications of big data inference were also presented. In this talk, I will describe those challenges and tools that stood out frequently and will summarize some examples of application that were presented during Opening Conference and Boot Camp. This work is based on a paper (in press for ISI Review) that has been written by the postdoctoral fellows and long-term visitors of the Fields institute that participated in the Big Data Program.