Electrostatic vibration energy harvesters (e-VEHs) are systems that convert part of their surroundings' kinetic energy into electrical energy, in order to supply small-scale electronic systems. Inertial E-VEHs are comprised of a mechanical subsystem that revolves around a mobile mass, and of an electrical interface. The mechanical and electrical parts are coupled by an electrostatic transducer. This thesis is focused on improving the performances of e-VEHs by the design of their electrical interface. The first part of this thesis consists in the study of a family of electrical interfaces called charge-pumps conditioning circuits (CPCC). It starts by building a formal theory of CPCCs. State-of-the-art reported conditioning circuits are shown to belong to this family. This family is then completed by a new CPCC topology. An electrical domain comparison of different CPCCs is then reported. Next, a semi-analytical tool allowing for the comparison of CPCC-based e-VEHs accounting for electromechanical effects is reported. The first part of the thesis ends by presenting a novel method for the measurement of e-VEHs' built-in electret potential. The second part of the thesis presents a radically different design approach than what is followed in most of state-of-the-art works on e-VEHs. It advocates for e-VEHs that actively synthesize the dynamics of their mobile mass through their electrical interface. We first show that this enables to convert energy in amounts approaching the physical limits, and from arbitrary types of input vibrations. Then, a complete architecture such an e-VEH is proposed and tested in simulations submitted to human body vibrations.