Recent studies of DNA axis curvature and flexibility based on molecular dynamics (MD) simulations on DNA are reviewed. The MD simulations are on DNA sequences up to 25 base pairs in length, including explicit consideration of counterions and waters in the computational model. MD studies are described for ApA steps, A-tracts, for sequences of A-tracts with helix phasing. In MD modeling, ApA steps and A-tracts in aqueous solution are essentially straight, relatively rigid, and exhibit the characteristic features associated with the B'-form of DNA. The results of MD modeling of A-tract oligonucleotides are validated by close accord with corresponding crystal structure results and nuclear magnetic resonance (NMR) nuclear Overhauser effect (NOE) and residual dipolar coupling (RDC) structures of d(CGCGAATTCGCG) and d(GGCAAAAAACGG). MD simulation successfully accounts for enhanced axis curvature in a set of three sequences with phased A-tracts studied to date. The primary origin of the axis curvature in the MD model is found at those pyrimidine/purine YpR "flexible hinge points" in a high roll, open hinge conformational substate. In the MD model of axis curvature in a DNA sequence with both phased A-tracts and YpR steps, the A-tracts appear to act as positioning elements that make the helix phasing more precise, and key YpR steps in the open hinge state serve as curvature elements. Our simulations on a phased A-tract sequence as a function of temperature show that the MD simulations exhibit a premelting transition in close accord with experiment, and predict that the mechanism involves a B'-to-B transition within A-tracts coupled with the prediction of a transition in key YpR steps from the high roll, open hinge, to a low roll, closed hinge substate. Diverse experimental observations on DNA curvature phenomena are examined in light of the MD model with no serious discrepancies. The collected MD results provide independent support for the "non-A-tract model" of DNA curvature. The "junction model" is indicated to be a special case of the non-A-tract model when there is a Y base at the 5' end of an A-tract. In accord with crystallography, the "ApA wedge model" is not supported by MD.