The analysis of modern massive data sets is a topic of contemporary interest in statistics, data science and machine learning. Understanding and extracting associations and dependencies is an important topic in modern statistical analysis. In this talk we consider the problem of correlation estimation, testing and graphical model selection when the number of features by far exceeds the number of samples. We consider various methods with a view to understanding which ones are appropriate for various sample size and dimension regimes. In particular, we aim to understand the strengths and drawbacks of methods for handling high dimensional parameters. (Joint work with A.O. Hero, University of Michigan, Ann Arbor)