Mean flows, ocean diffusivity, and relative dispersion are fundamental quantities that have been estimated from quasi-Lagrangian observations for over five decades. In the last three decades, a number of velocity statistics and diffusivity estimates have been calculated from ocean drifters and floats from larger and larger data sets. These studies have indicated that it is not a trivial exercise to estimate these quantities, even from large drifter sets such as those in the Gulf of Mexico. The large spatio-temporal variability in observed average velocities and diffusivity estimates indicates that classical theory, while elegant in the mathematical world, does not adequately describe the real world. These estimates and any climatological estimates are of little use for operational, real-time numerical simulations of ocean dispersion, given that the diffusivity is a strong function of dynamical features, wind forcing, and topography. Nevertheless, Taylor-based estimates can provide order of magnitude estimates of diffusivity. Mean velocity and dispersion estimates computed from drifter data sets suggest that a new paradigm is needed for ocean dispersion that does not depend on stationary flow in homogeneous domains and on the subjective decomposition into mean and fluctuating components, but accounts for different dynamical features and their interactions.