Whereas most blind source separation (BSS) and blind mixture identification (BMI) investigations concern linear mixtures (instantaneous or not), various recent works extended BSS and BMI to nonlinear mixing models. They especially focused on two types of models, namely linear-quadratic ones (including their bilinear and quadratic versions, and some polynomial extensions) and post-nonlinear ones. These works are particularly motivated by the associated application fields, which include remote sensing, processing of scanned images (show-through effect) and design of smart chemical and gas sensor arrays. In this paper, we provide an overview of the above two types of mixing models and of the associated BSS and/or BMI methods and applications.9237 155167