Since the discovery of brown dwarfs in 1994, and the discovery of dust cloud formation in the latest Very Low Mass Stars (VLMs) and Brown Dwarfs (BDs) in 1996, the most important challenge in modeling their atmospheres as become the understanding of cloud formation and advective mixing. For this purpose, we have developed radiation hydrodynamic 2D model atmosphere simulations to study the formation of forsterite dust in presence of advection, condensation, and sedimentation across the M-L-T VLMs to BDs sequence (Teff = 2800 K to 900 K, Freytag et al. 2010). We discovered the formation of gravity waves as a driving mechanism for the formation of clouds in these atmospheres, and derived a rule for the velocity field versus atmospheric depth and Teff, which is relatively insensitive to gravity. This rule has been used in the construction of the new model atmosphere grid, BT-Settl, to determine the micro-turbulence velocity, the diffusion coefficient, and the advective mixing of molecules as a function of depth. This new model grid of atmospheres and synthetic spectra has been computed for 100,000 K > Teff > 400 K, 5.5 > logg > -0.5, and [M/H]= +0.5 to -1.5, and the reference solar abundances of Asplund et al. (2009). We found that the new solar abundances allow an improved (close to perfect) reproduction of the photometric and spectroscopic VLMs properties, and, for the first time, a smooth transition between stellar and substellar regimes -- unlike the transition between the NextGen models from Hauschildt et al. 1999a,b, and the AMES-Dusty models from Allard et al. 2001. In the BDs regime, the BT-Settl models propose an improved explanation for the M-L-T spectral transition. In this paper, we therefore present the new BT-Settl model atmosphere grid, which explains the entire transition from the stellar to planetary mass regimes.