This chapter focuses on next-generation selection models that allow us to expand on the Heckman model using copula and control function models that allow one to estimate selection models for a large range of other statistical distributions. This chapter also shows how to generate weights that account for nonignorable nonresponse; not only do these weights increase the weight on demographic groups that respond with lower probabilities, they also increase weights on people with opinions that may make them less inclined to respond. This chapter also shows how to modify a Heckman model to allow for estimation of a nonignorable nonresponse selection model when we have a response-related variable that is available only for people in the survey sample.