Today's vehicle must be efficient in terms of gas (CO2, NOx) emissions and fuel consumption. Due to improvements in material and oil, the continuous variable transmission (CVT) is now making a breakthrough in the automotive market. The CVT decouples the engine from the wheel speed. CVT enables significant fuel gains by shifting the engine operating point for specific power demands. This optimization of the operating point enables a reduction of this fuel consumption. A CVT is constituted of two pulley sheaves, one fixed and the other one movable in its axial direction when subjected to an external axial force, in general hydraulic. The transition from the minimum to the maximum speed ratio is continuous and an infinite numbers of ratio is available between these two limits. An intermediate element (a metallic belt or chain) transmits the power from the input (the primary) to the exit (the secondary) of the CVT or variator. Further improvements of the fuel consumption and gas emission are still required for example by improving the variator efficiency. Increasing hydraulic performance or decreasing mechanical losses by reducing the axial forces are some solutions. The latter method is not without risks. The diminution of the clamping forces increases the slip between pulley sheaves and the intermediate element. If the axial forces decrease too much, high slip values can be reached and cause damage to the pulleys and the intermediate element. Control of the slip is an attractive solution to decrease the clamping forces in order to safely improve the variator efficiency. The objective of this thesis is to understand and model the slip of each pulley and establish analytic tools dedicate to the variator control. The slip study and the theoretical approach of the CVT variator is applied to the slip control of the variator with a chain. The contribution of this work is threefold. Firstly, the slip and the traction coefficient are analyzed for each pulley. The slip analysis of each pulley is then used to define a new slip synthesis as the summation of the slip of each pulley. It is demonstrated that the slip and the traction coefficient are different for each pulley and depend on the speed ratio of the variator. In low ratios, both the secondary pulley and the primary pulley slip, but only the primary reaches macro slip. For middle or higher ratios, only the secondary pulley slips and reaches high values of slip. Experiments show that the pulley with the smallest clamping force limits the system. Secondly, based on kinematics, force equilibrium, elastic deformations of the pulleys and the intermediate element, a detail model of the variator is proposed. The principal results are the estimation of the clamping forces, of the traction curve for each pulley and of the chain efficiency. These results are implemented in a simpler model that describes the variator dynamics. This last model considers the two pulleys and the intermediate element as free bodies. The hydraulic circuit and the actuators, which are important to take into account for control, are also modeled. Thirdly, the new slip synthesis and the results of the dynamic models are applied to the slip control of the variator in order to improve the efficiency. A pole placement law is applied to the actuators to control the flow that enters or exits the pulleys. With this law, the actuators are decoupled and the bandwidth is increased sufficiently for actuators dynamics to be neglected. The primary and the secondary pressures are decoupled and linearized by an input-output feedback linearization. The resulting system is linear and linear control theory can be applied to control the two pressures. The speed ratio is controlled by the primary clamping force. The secondary pressure is chosen as a function of the control mode of the variator: standard mode or slip mode. In standard mode, the intermediate element is overclamped by 30%, whereas in slip mode, the secondary clamping force is set as a function of the desired slip. By controlling the slip at 2%, the mechanical efficiency was increased by more than 2% and the clamping forces reduced by more than 30%. For the slip control, a proportional-integrator law and a model reference adaptive control (MRAC) are presented and the performances compared. The MRAC gives slightly better results.