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Accreting black holes and neutron stars in their hard (low) state show notonly very similar X/gamma-ray spectra but also that the behaviour of theirlight curves is quite similar which can be quantified as having similarpower-density spectra and Fourier-frequency-dependent time/phase lags. Takentogether this argues for a common mechanism of the X/gamma-ray production inthese objects. This mechanism is probably a property of the accretion flow onlysince it does not depend on the nature of the compact object. In this paper, Ireview the observational data paying most attention to the properties of thetemporal variability such as the time/phase lags that hopefully can help us todiscriminate between different theoretical models. I also discuss the modelsdeveloped to account for the basic observational facts. Particularly, I showthat the commonly used Compton cloud models with constant temperature cannotexplain variable sources without violating the energy conservation law.Alternative models where time lags are related to the spectral evolution duringX-ray flares are discussed and compared with observations. Compton reflectionfrom the outer edge of the accretion disc is shown to markedly affect the timelag Fourier spectrum.Comment: 16 pages; invited talk at the meeting "X-ray Astronomy 1999: Stellar  Endpoints, AGN and the Diffuse Background", held in Bologna, Italy, September  199

Time lags in compact objects: Constraints on the emission models