The degree of complexity of physics due to proximity effects in close binary stars is one of the most important challenges in theoretical stellar physics. The knowledge of how the specific intensity is distributed over the stellar disk is primordial to model the light curves of eclipsing binaries and planetary transits correctly. In order to provide theoretical input for light curve modelling codes, we present new calculations of gravity- and limb darkening coefficients for a wide range of effective temperatures, gravities, metallicities and microturbulent velocities. We have computed limb darkening coefficients for several atmosphere models, covering the transmission curves of the Kepler, CoRoT and Spitzer space missions as well as more widely used passbands (Stroemgren, Johnson-Cousins, Sloan). In addition to these computations, which were computed by adopting the Least-Square Method, we also performed calculations for the bi-parametric approximations by adopting the Flux Conservation Method to provide users with an additional tool to estimate the theoretical error bars. To facilitate the modelling of the effects of tidal and rotational distortions, we computed the GDCs y({lambda}) using the same models of stellar atmospheres as in the case of limb-darkening. Compared to previous work, a more general differential equation was used which now takes into account local gravity variations and the effects of convection. The limb darkening coefficients were computed with a larger numerical resolution (100um points instead of 15 or 17 as is often used in the ATLAS models) and five equations were used to describe the specific intensities (linear, quadratic, root-square, logarithmic and a 4-coefficient law (Equation 5)). Concerning the GDCs, the influence of the local gravity on y({lambda}) is shown as well as the effects of convection, which turn out to be very significant for cool stars. The results are tabulated for log(g)'s ranging from 0.0 to 5.0,-5.0<=log[M/H]<=+1, 2000K<=Teff<=50000K and for 5 values of the microturbulent velocity (0, 2, 4, 6, 8). ATLAS and PHOENIX plane-parallel atmosphere models were used for all the computations.