Aortic valve repair (AVr) has evolved into a reproducible surgical strategy for selected patients with aortic regurgitation (AR), offering preservation of native tissue, avoidance of prosthesis-related complications, and favorable long-term outcomes when performed at expert centers. This narrative review summarizes contemporary concepts, indications, preoperative imaging work-up, and procedure selection for AVr in tricuspid (TAV) and bicuspid (BAV) aortic valves, with an emphasis on functional mechanisms and standardized annular and root stabilization. Recent international guidelines and key surgical series and registries addressing aortic valve repair, valve-sparing root replacement (VSRR), annuloplasty strategies, and bicuspid repair techniques were reviewed. Modern AVr is anchored in mechanism-based diagnosis of AR, systematic correction of cusp pathology, and stabilization of the functional aortic annulus (FAA), including the virtual basal ring, sinotubular junction, and aortic root. Current guideline recommendations support aortic valve repair in selected patients with severe AR at experienced centers when durable results are expected and recommend valve-sparing root replacement in young patients with aortic root dilation. Quantitative intraoperative quality control, including effective height targets, and durable annular stabilization are key determinants of repair longevity. AVr and VSRR represent mature surgical options for carefully selected patients with AR, particularly younger individuals with good cusp tissue and access to high-volume repair expertise. A mechanism-driven algorithm, including BAV-specific geometry restoration approaches such as the 180-degree reimplantation technique, may clarify the optimal procedure for each clinical scenario.