The aim of this talk is to give an update on recent achievements and developments on rigid compact complex manifolds. I will start introducing different notions of rigidity and explaining the relations among them. For curves all these notions coincide and the only rigid curve is the projective line. For surfaces rigidity is still quite „rare", since the only rigid surfaces which are not minimal of general type are Del Pezzo surfaces of degree at least 5 and Inoue surfaces. In higher dimension the geography of rigid manifolds gets much richer. Then I will report on an answer to a more than 40 years open question of Morrow and Kodaira, exhibiting an infinite series of rigid but not infinitesimally rigid surfaces of general type. I will conclude addressing open questions and conjectures. [cite: https://www.google.com/search?q=20, 161]