Empirical constraints on turbulence in proto-planetary discs

roto-planetary discs, the birth environment of planets, are an example of a structure commonly found in astrophysics, accretion discs. Identifying the mechanism responsible for accretion is a long-standing problem, dating back several decades. The common picture is that accretion is a consequence of turbulence, with several instabilities proposed for its origin. While traditionally this field used to be a purely theoretical endeavour, the landscape is now changing thanks mainly to new observational facilities such as the ALMA radio interferometer. Thanks to large improvements in spatial and spectral resolution and sensitivity (which have enabled the study of disc substructure, kinematics and surveys of large disc populations), multiple techniques have been devised to observationally measure the amount of turbulence in discs. This review summarises these techniques, ranging from attempts at direct detection of turbulence from line broadening, to more indirect approaches that rely on properties of the dust or consider the evolution of global disc properties (such as masses, radii and accretion rates) for large samples, and what their findings are. Multiple lines of evidence suggest that discs are in fact not as turbulent as thought one decade ago. On the other hand, direct detection of turbulence in some discs and the finite radial extent of dust substructures and in some cases the finite vertical extent strongly indicate that turbulence must be present at some level in proto-planetary discs. It is still an open question whether this amount of turbulence is enough to power accretion or if this is instead driven by other mechanisms, such as MHD winds.