The use of optimization as a framework for formulating machine learning problems has become much more widespread in recent years. In some cases, the demands of the machine learning problems go beyond the scope of traditional optimization paradigms. While existing optimization formulations and algorithms serve as an good starting point for the solution strategies, important work must be carried out at the interface of optimization and machine learning to devise strategies that exploit the special features of the application and that perform well on very large data sets. This talk reviews recent developments from an optimization perspective, focusing on activity during the past three years, and looking in particular at problems where the machine learning application has motivated novel algorithms or analysis in the optimization domain. We also discuss some current challenges, highlighting several recent developments in optimization that may be useful in machine learning applications.