Regression surfaces can also exhibit non-smooth or irregular features. To recover e.g. a non-smooth behaviour one should avoid using a nonparametric technique that smooths away this particular behaviour. We discuss how to estimate via local linear fitting a non- smooth regression surface, in case of fixed or random design. The proposed procedure can also be used for image denoising. Applications to surface estimation and image denoising are shown. Sometimes the interest is in estimating the location of the points/curves at which e.g. a function is non-smooth, say discontinuous. This relates to the problem of change-point estimation or edge detection (or boundary estimation). We discuss how one can use the previously discussed techniques to some other problems, such as estimating non-smooth densities. These lectures are partly based on joint work with Alexandre Lambert and Peihua Qiu.