Translating solitons, or translators for short, are self-similar solutions of the mean curvature flow which evolve by translation over a fixed direction. In this talk we will review some basic facts about these translators. Moreover, we will describe the construction of new examples of complete, properly embedded translating annuli in Euclidean space. The surfaces, which we call annuloids, are contained in vertical slabs and are not surfaces of revolution. We also provide new examples of complete, simply connected translators.