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The development of very high-speed motors has evolved fascinatingly in the last few years. Due to their speed, their low weight and their high power density, the need for such motors has recently increased for various different applications. Among them, superchargers or turbochargers can be cited in the automotive industry, as well as vacuum cleaners in the home appliance industry, machine tools or drilling machines in the machining industry. However, the development of very high-speed motors remains a big challenge. Indeed because of the high mechanical stress in the rotor and the high power density, a precise understanding of the electromagnetic, mechanic and electrical behavior becomes crucial. In order to gain as much understanding of the problem as possible, this thesis is entirely focused on analytical approaches and the results are validated with finite element methods, as well as measurements on a prototype with 200'000 rpm and 2 kW of target of speed and output power. Due to its high efficiency, a slotless structure was chosen and all the present work relates to this type of motor. This thesis can be divided in three parts. The first part deals with the design of the different analytical models (electromagnetical, aerodynamical and mechanical). The electromagnetic model is based on the vector potential generalized diffusion equation which allows a much more precise calculation of the fields than the widely used equivalent Kirchhoff circuit approach. The electromagnetic torque, the self and mutual inductances and the eddy current power losses are deduced. These different calculated quantities are in excellent agreement with finite element methods. A model of eddy current power losses in the windings is also given. The main contributions of the electromagnetic model are the following. The magnetic vector potential is given analytically in a structure of any number of concentric cylindrical layers. It is useful for other structures than slotless permanent-magnet motors such as, for example, eddy current brakes. Moreover, the power losses in the rotor are given explicitly in term of the vector potential harmonics in the air gap. Furthermore, the power losses can be calculated explicitly in permanent magnets with various magnetization harmonic contents. The other aspects of the multiphysics model are also modeled analytically: the aerodynamic power losses, the bearing power losses and the mechanical stresses in the rotor. Furthermore, an electrical model of the currents is given. It includes both 120° and 180° inverter commutation sequences. The second part deals with the optimization using the model for obtaining a design. As the model is analytical, the optimization process is very fast. It also allows to draw Pareto frontiers. The final part deals with the construction of a prototype, the design of measurements techniques compatible with very high speeds and the validation of the different models. Not only does this part validates the models, but it also shows that the designed prototype is able to exceed the speed target of 200'000 rpm and output power target of 2 kW.