This review elucidates the comparative applications of elliptical closures and S-plasty or “lazy s” in the excision of cutaneous neoplasms on the extremities. The article completes an analysis of closure techniques by discussing their merits, limitations, and optimal applications based on their orientation and tension dynamics. It also provides a detailed guide on suture placement and specific intraoperative maneuvers associated with the S-plasty to enhance surgical outcomes. The S-plasty, preferred for its diminished suture line tension and adaptability to convex areas, is analyzed against traditional relaxed skin tension lines and the emerging biodynamic excisional skin tension (BEST) lines. The review underscores the BEST lines’ role in minimizing perpendicular traction and their impact on improved surgical outcomes on the extremities. It also addresses the challenges of excessive traction along wound margins and the consequential suboptimal healing outcomes, emphasizing the importance of appropriate tension management. This review also compares the stability, efficiency, and esthetic outcomes of the S-plasty with elliptical excisions, highlighting the S-plasty’s superior ability to distribute tensile forces evenly, thus reducing the risk of scar-related complications. It also discusses the benefits of using BEST lines for tension vector dispersion coupled with the design of an S-plasty, even when relaxed skin tension line favors a horizontal orientation. Furthermore, the review elaborates on the procedural execution of the S-plasty, emphasizing the importance of precise suture placement and selecting suitable suture materials and techniques to ensure optimal wound edge perfusion. The overarching theme is the prioritization of technique based on specific anatomic considerations and the surgeon’s expertise to ensure the most effective and beneficial cutaneous excisions on the extremities.