The classical results of Lorenz (1969) suggest that regardless of the quality of observations and forecast models, flows with many scales of motion may have finite, intrinsic limits of predictability, owing to the increase of error growth rates as scale decreases. Lorenz's results, along with those of more sophisticated turbulence-closure models, indicate that predictability will be intrinsically limited in three-dimensional turbulence, but not in the forward cascading inertial range of two-dimensional turbulence. Increased computational capabilities now allow direct investigation of the growth of forecast differences in flows that truly span multiple scales of motion. The atmospheric mesoscale represents a particularly interesting case, as it is complicated by the importance of moist convection and lies at the transition between regimes that in some respects resemble two-dimensional and three-dimensional turbulence. We will review the concept of an intrinsic limit of predictability and discuss recent efforts to quantify and understand error growth in simulations of midlatitude cyclones with explicitly resolved moist convection and in high-resolution simulations of quasigeostrophic turbulence.