The detection of the warm inner part of debris discs---the extrasolar counterparts of the zodiacal cloud---is of prime importance to characterise the global architecture of planetary systems. Because of the high contrast and small angular separation between the star and the exozodiacal light, high-precision infrared interferometry is the best-suited tool to carry out such observations. In this paper, we review the first detection of an exozodiacal disc by this method recently reported around Vega by Absil et al. (2006), and discuss the currently on-going observing efforts in this domain. We show how interferometric data can give access to the composition and the dynamics (including LHB-like events) of extrasolar planetary systems, and thereby put useful constraints on the presence of small bodies and/or giant planets. This statement is illustrated with new data obtained on various bright Vega-type stars, including Vega itself. Finally, we show how the new generation of interferometric instruments will change our view of debris discs: with their increased sensitivity and imaging capabilities, they will constrain the morphology of bright exozodiacal discs and push the detection limit towards meaningful density levels in the context of future life-finding missions such as Darwin/TPF.