Over the past fifty years, building on the pioneering works of Lawden and Edelbaum, we have benefited immensely from their insights and notional algorithms for optimal spacecraft orbit transfers using continuous and impulsive thrust. Their results remain relevant and are of both theoretical and practical significance. Edelbaum contributed important insights for impulsive transfers, showing that multiple impulses are often superior to the Lambert two-impulse transfers with regard to minimization of DV. However, Edelbaum’s work, while insightful, does not answer his question for general problems: How many impulses? In this presentation, building upon the framework of Lawden’s theory, a new construct – optimal switching surfaces – are introduced that serve as an illuminating interactive construct, which unifies two of the seemingly disparate types of maneuvers, namely, impulsive and low-thrust maneuvers. The topography of these optimal switching surfaces allow us to efficiently sweep over an infinite set of maximum thrust values and find the critical points where bang-bang, bang-off-bang switching for coasts sub-arcs and related behaviors occur. In addition to the optimal switching surfaces, I will review the application of a new framework developed to deal with the problem of designing optimal control for systems that have multiple modes of operation. Notable examples of such systems, in space applications, could be a spacecraft equipped with 1) a thruster that can vary its specific impulse and thrust level simultaneously, or switch between distinct discrete operating modes or 2) multiple thrusters that can independently be switched on/off depending on available power and/or optimality criteria. The proposed framework reduces the original complex multiple-point boundary-value problems to smooth, differentiable two-point boundary-value problems; the latter is notably easier to solve. I will present the application of the proposed framework to design fuel-optimal trajectories from the Earth to comet 67P.