Transcatheter aortic valve implantation (TAVI) has, in less than 20 years, become the dominant interventional treatment for aortic stenosis in developed countries. Its development has been characterised by the growth of procedural expertise and device improvement. Every aspect of this therapy has been investigated, increasing clinical evidence and leading to continued optimisation. The purpose of this review article is to provide an overview of the rapidly changing field of TAVI therapy, briefly describing key past achievements and discussing residual challenges.