In observational studies of causal effects, matching methods are widely used to approximate the ideal study that would be conducted under controlled experimentation. In this talk, I will discuss new matching methods that use tools from modern optimization to overcome five limitations of standard matching approaches. In particular, these new matching methods (i) directly obtain flexible forms of covariate balance, as specified before matching by the investigator; (ii) produce self-weighting matched samples that are representative of target populations by design; and (iii) handle multiple treatment doses without resorting to a generalization of the propensity score. (iv) These methods can handle large data sets quickly. (v) Unlike standard matching approaches, with these new matching methods typical estimators are root-n consistent under the usual conditions. I will illustrate the performance of these methods in an epidemiology case study about the impact of an earthquake on post-traumatic stress.