Whether the 3D Navier-Stokes equations have regular solutions for arbitrary long times has been an enduring problem since the time when Jean Leray (1934) set out his ideas on weak solutions. After more than a century, conventional methods appear to have been exhausted. My talk will summarize a set of numerical experiments that suggest that nonlinear depletion in 3D-NS dynamics is very strong. In this context, solutions appear to operate in a regular regime. It is shown that two other regimes theoretically exist, one of which corresponds to weak solutions but neither of these appear to be represented in the dynamics. However, a transition between the three cannot be discounted.