In spite of the noninferiority of transcatheter aortic valve replacement (TAVR) in high- and intermediate-risk patients, there are still obstacles that need to be overcome before the procedure is further expanded and clinically integrated. The lack of evidence on the long-term durability of the bioprostheses used for TAVR remains of particular concern. In addition, surgery may be preferred over TAVR in patients with bicuspid aortic valve (BAV) or with concomitant pathologies such as other valve diseases (mitral regurgitation/tricuspid regurgitation), aortopathy, and coronary artery disease. In this review, we discuss and summarize relevant data from clinical trials, current trends, and remaining obstacles, and provide our perspective on the indications for the expansion of TAVR.