Abstract: The success of nuclear fusion requires optimal magnetic fields. These should provide the necessary plasma performance to sustain high temperature plasmas for a long enough time period. However, there are still important outstanding issues in magnetic fusion, such as the understanding and control of plasma density, fast particles and heat diffusion. To achieve good confinement, recent stellarator devices such as HSX and W7-X have been designed using optimization based on the calculation of 3D MHD equilibria at each evaluation of the objective function. In here, we show how new design methods have been able to reduce the computational cost of such optimization efforts by orders of magnitude, while also providing new insights into the space of solutions. These methods enable a direct geometrical construction of magnetic fields with extremely good confining properties such as quasisymmetry and quasi-isodynamic fields. Thanks to the reduced computational cost, we are able to achieve good particle confinement to much higher accuracy than reported before and perform wide surveys over parameter space. Furthermore, many figures of merit can be now calculated directly, including MHD stability and all the geometric quantities in the gyrokinetic equation, making the design of a fusion machine optimized for turbulent transport and fast particles a possibility in the near future.