This paper presents a method for computing planar gluon scattering amplitudes at strong coupling in N = 4 super Yang-Mills theory using the gauge/string duality. The computation involves finding a classical string configuration whose boundary conditions are determined by the gluon momenta. The results are infrared divergent, and the paper introduces a gravity version of dimensional regularization to define finite quantities. The leading and subleading infrared divergences are characterized by functions of the coupling that are computed at strong coupling. The full finite form for the four-point amplitude is computed and found to agree with a recent conjecture by Bern, Dixon, and Smirnov. The paper discusses the structure of infrared divergences and their relation to the cusp anomalous dimension. It also describes the computation of the four-point amplitude using the AdS/CFT correspondence, finding a classical string solution that ends on a sequence of lightlike segments. The solution is regularized using dimensional regularization, and the action is evaluated to extract the finite parts of the amplitude. The results are compared with field theory predictions, showing agreement with the conjecture of Bern, Dixon, and Smirnov. The paper concludes that the structure of infrared divergences is consistent with general field theory expectations and that the results provide a strong coupling form for the functions characterizing the subleading divergent terms. The paper also discusses the potential for further studies of higher-point amplitudes and the use of integrability in computing scattering amplitudes as a function of the coupling.This paper presents a method for computing planar gluon scattering amplitudes at strong coupling in N = 4 super Yang-Mills theory using the gauge/string duality. The computation involves finding a classical string configuration whose boundary conditions are determined by the gluon momenta. The results are infrared divergent, and the paper introduces a gravity version of dimensional regularization to define finite quantities. The leading and subleading infrared divergences are characterized by functions of the coupling that are computed at strong coupling. The full finite form for the four-point amplitude is computed and found to agree with a recent conjecture by Bern, Dixon, and Smirnov. The paper discusses the structure of infrared divergences and their relation to the cusp anomalous dimension. It also describes the computation of the four-point amplitude using the AdS/CFT correspondence, finding a classical string solution that ends on a sequence of lightlike segments. The solution is regularized using dimensional regularization, and the action is evaluated to extract the finite parts of the amplitude. The results are compared with field theory predictions, showing agreement with the conjecture of Bern, Dixon, and Smirnov. The paper concludes that the structure of infrared divergences is consistent with general field theory expectations and that the results provide a strong coupling form for the functions characterizing the subleading divergent terms. The paper also discusses the potential for further studies of higher-point amplitudes and the use of integrability in computing scattering amplitudes as a function of the coupling.