Capacitive electrocardiogram (cECG) systems are increasingly used for the monitoring of cardiac activity. They can operate within the presence of a small layer of air, hair or cloth and do not require a qualified technician. They can be integrated into wearables, clothing or objects of daily life, such as beds or chairs. While they offer many advantages over conventional electrocardiogram systems (ECG) that rely on wet electrodes, they are more prone to be affected by motion artifacts (MAs). These effects, which are due to the relative movement of the electrode in relation to the skin, are several orders of magnitude higher than ECG signal amplitudes, they occur in frequencies that might overlap with the ECG signal, and they may saturate the electronics in the most severe cases. In this paper, we provide a detailed description of MA mechanisms that translate into capacitance variations due to electrode-skin geometric changes or into triboelectric effects due to electrostatic charge redistribution. A state-of-the-art overview of the different approaches based on materials and construction, analog circuits and digital signal processing is provided as well as the trade-offs to be made using these techniques, to mitigate MAs efficiently.