Transcatheter aortic valves (TAVs) represent the latest advances in prosthetic heart valve technology. TAVs are truly transformational as they bring the benefit of heart valve replacement to patients that would otherwise not be operated on. Nevertheless, like any new device technology, the high expectations are dampened with growing concerns arising from frequent complications that develop in patients, indicating that the technology is far from being mature. Some of the most common complications that plague current TAV devices include malpositioning, crimp-induced leaflet damage, paravalvular leak, thrombosis, conduction abnormalities and prosthesis-patient mismatch. In this article, we provide an in-depth review of the current state-of-the-art pertaining the mechanics of TAVs while highlighting various studies guiding clinicians, regulatory agencies, and next-generation device designers.