Nowadays, there is a very high number of electronic devices with different ranges of power. Desktop peripherals and cellphones are an example of widely used low power devices. Contactless power transfer is useful to supply or recharge these devices without any physical link. Their lifetime can be increased because wires are a source of dysfunction. Contactless power transfer is also very useful in supplying rotating parts. Indeed, the brushes typically used for this purpose are impractical for high speed applications and are also a source of dysfunction. In recent years, the development of electric vehicles became a great opportunity for contactless power transfer applications. The batteries of these vehicles have a limited autonomy which makes the charging process very important. By taking as a starting point, the contactless battery charging for an electric vehicle, this work addresses contactless power transfer using inductive couplers. The modelling proposed in the scope of this work is available for different ranges of power. However, special attention is given to crucial points for high power applications, which are the efficiency of the system and the radiated magnetic field. Indeed, the efficiency in high power transfer is a crucial point for ecological and thermal dissipation reasons. The radiated field must be limited to meet magnetic radiation guidelines and to ensure the safety of users. The inductive coupled power transfer (ICPT), similar to a conventional transformer, is made of two magnetically coupled coils. The first one, called the primary coil, is supplied with an alternating current, which induces a voltage in the secondary coil. The amplitude of the induced voltage in the secondary coil is a function of the magnetic coupling factor and the operating frequency. The main difference between conventional transformers and inductive couplers is the value of the magnetic coupling. Indeed, the distance between the coils is larger for inductive couplers, and the magnetic field lines are not guided by a ferromagnetic material as in the case in conventional transformers. As a result, such a system is also called an "air-transformer". To obtain high performance in spite of a very low coupling factor (typically $0.1$ compared to $0.9$), compensation capacitances are inserted into the system. They compensate the very low power factor due to the magnetisation of the inductances. The different compensation topologies are studied and compared in detail in this work. They determine the load characteristic, the frequency response and the values of the voltages and currents in the coils. A novel compensation methodology is proposed and compared to the existing one. It aims to simplify the transformer's control instead of maximizing the efficiency. When a conductive plate is close to the transformer, Eddy currents are induced leading to the generation of Joule losses. The system efficiency is thus decreased and thermal dissipation becomes an issue. In this case, adding magnetic shielding to the structure is very efficient. A modelling of these effects is performed and several shielding topologies are proposed. An optimisation of the shielding geometry, based on genetic algorithms, is also undertaken.