The graphical model formalism allows to describe multivariate probability distributions using a graph where random variables are represented by nodes, and the absence of an edge corresponds to conditional independence. While this formalism is very general, the corresponding maximum-likelihood problem is often challenging numerically. In addition, one often needs to obtain a graph that is sparse, in order to enhance interpretability of the result. In this talk, we examine the problem where log-likelihood function is penalized by an l-one norm term to encourage sparsity, in two special cases,first for Gaussian then for Boolean variables. In the Gaussian case, we discuss first-order methods and a block- coordinate descent algorithm. For Boolean random variables, the problem is NP-hard, due to an exponential number of terms in the log-likelihood function. We discuss two approximations, one based on Wainwright and Jordan's log- determinant approximation (2005), and another based on lifting and rank relaxation.