Over the last two decades, a large number of electron storage rings have been built around the world, which are running as dedicated light sources with the use of insertion devices. One of their primary performance indicating figures of merit is the flux intensity of the generated synchrotron radiation, which is directly related to the beam current of the circulating electrons. The present talk shall address the general beam dynamics limitations associated with increasing the beam current in 3rd generation light sources, which mostly appear in the form of collective beam instability. It basically consists in the beam interacting with its self-induced electromagnetic fields, conventionally described as the coupling impedance. An emphasis shall be placed on the enhanced sensitivity of many light sources to instability due to strong focusing of the beam and the presence of numerous low-gap insertion devices. As specific examples, studies made at SOLEIL shall be introduced. Starting from the impedance calculation and minimisation, as well as instability predictions on the basis of the former, carried out at the machine design stage, the measurement and analysis of the instabilities actually observed on the machine shall be presented. The talk shall also refer to the simulation, analytical and diagnostic tools developed for this purpose.