Efficiency is a critical consideration in the design of turbines. A computational study has been conducted, using steady and unsteady three-dimensional Reynolds-Averaged Navier-Stokes computations, to improve the maximum efficiency of crossflow hydro turbines that are typically used for small-scale, low-head remote power systems. Although these turbines are simple to design and manufacture at low cost, a longstanding technical problem is their lower maximum efficiency than their more advanced counterparts, such as Pelton and Francis. Despite an inherently simple design, the flow field inside the crossflow turbine is highly complex. Since internal flow physics govern the turbine performance, major emphasis is put on understanding the important performance limiting flow mechanisms as an aid for improving the efficiency. The study follows a direct design method, which involves defining the turbine configurations, computing the flow field, and modifying the design by synthesizing the information obtained from the computed flow fields to improve the design. Toward this goal, computations were performed on two small-scale turbines whose performance was experimentally determined, one with 69% efficiency and the other with 88% efficiency. The findings of the simulations were synthesized to identify the key design problem and define an optimum turbine configuration. Then detailed computations were performed on varying turbine configurations for establishing the qualitative and quantitative links between the geometric parameters and the key flow features and understanding their roles on turbine performance. A critical part of the analysis involves matching two main components, the nozzle and the impeller, in order to achieve higher efficiency. For the nozzle design, a simple two-dimensional analytical model was developed with the intention of converting all the turbine head into kinetic energy at the impeller inlet and computing approximately the nozzle geometrical parameters as a guide for computationally intensive simulations. Systematic computations were performed on a realistic design problem, which is the matching of the nozzle and the impeller designs in the reference turbines mentioned above. The results showed that crossflow turbines can achieve efficiencies more than 90%, computed efficiency of which is a significant improvement in the existing design. An example turbine design with 91% efficiency has been achieved for the original 69% efficient turbine.