Parametric and nonparametric models are convenient mathematical tools to describe characteristics of data with different degrees of simplification. When a model is to be selected from a number of parametric candidates, not surprisingly, differences occur when the data generating process is assumed to be parametric or nonparametric. In this talk, in a regression context, we will consider the question if and how we can distinguish between parametric and nonparametric situations and discuss feasibility of adaptive estimation to handle both parametric and nonparametric scenarios optimally. A new model selection consistency result that can handle high dependence of the predictors will be presented as well. This is joint work with Wei Liu.