Several studies concerning the lateral torsional buckling of horizontally curved I-beams have been made by different researchers. However, these studies are mostly limited to linear analysis and involving only single girders having single span. Nonlinear analysis of horizontally curved I-beams have been very limited or almost none. The aims of this study are to give a brief summary of the studies that have been made involving several factors concerning the lateral torsional buckling capacity of horizontally curved I-beams and to show several analyses that focused on determining the behavior of the horizontally curved I-beams that experience lateral torsional buckling failure. Subjects discussed in this study include: (1) different design provisions involving LTB of curved I-beams; (2) different equations that can be used concerning LTB of curved I-beams; (3) effect of cross frames; (4) effects of cross frame spacing; and (5) analysis results and trends comparing LTB strength of curved I-beams to straight beams. The summary of these studies will be essential in determining the future studies that has to be made involving the lateral torsional buckling of horizontally curved I-girder bridges which should cover single girder and multi girder systems as well as single span and multi span curved bridge systems.