Information technology has enabled the collection of massive amounts of data in science, engineering, social science, finance and beyond. Statistics is the science of data and indispensable for extracting useful information from high-dimensional data. After broad successes of statistical machine learning on prediction through regularization, interpretability is gaining attention and sparsity is used as its proxy. With the virtues of both regularization and sparsity, L1 penalized Least Squares(e.g. Lasso) has been intensively studied by researchers from statistics, applied mathematics and signal processing. In this tutorial, I would like to give an overview of both theory and pratcice of Lasso and its extensions. I will review theoretical results of Lasso and M-estimation with decomposable penalties under high dimensional statistical models. I will also share experience on using sparse modeling methods in in two on-going projects in two very differnet areas. The first is an on-going collaborative project with the Gallant Neuroscience Lab at Berkeley on human understanding visual pathway. In particular, sparse models (linear, non-linear, and graphical) have been built to relate natural images to fMRI responses in human primary visual cortex area V1. Issues of model validation will be discussed. The second is the on-going StatNews project with the El Guaoui group in EECS at Berkeley where we use sparse methods to derive summaries of newspaper articles on a particular topic. We use human subject experiments to validate our findings.