The behaviour of sparse regularization using the Lasso method is well understood when dealing with discretized linear models. However, the behaviour of Lasso is poor when dealing with models with very large parameter spaces and in recent years, there has been much interest in the use of “off-the-grid” approaches, using a continuous parameter space in conjunction with the Blasso convex optimization problem over measures. I will discuss some topics in this area, including stability results, super resolution properties and also algorithms for this problem.