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Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently available commercial implementations of VMAT planning. In contrast, literature on the underlying mathematical optimization methods used in treatment planning is scarce. VMAT planning represents a challenging large scale optimization problem. In contrast to fluence map optimization in intensity-modulated radiotherapy planning for static beams, VMAT planning represents a nonconvex optimization problem. In this paper, the authors review the state-of-the-art in VMAT planning from an algorithmic perspective. Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed. Their advantages and limitations are outlined and recommendations for improvements are discussed. C 2015 American Association of Physicists in Medicine. [http://dx

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The authors used a digital phantom simulating a patient torso and 22 SBRT patients to show that the integral doses from the plans employing optimized non-coplanar beams are comparable to those of the coplanar plans using an equal number of discrete beams and are significantly lower than those of VMAT plans. The non-coplanar beams expose a larger normal tissue volume to non-zero doses, whose impact will need to be evaluated individually to determine the risk/benefit ratio of the non-coplanar plans.