NMR spectra of liquid crystalline phases and the molecules dissolved therein, spinning at and near the magic angle provide information on the director dynamics and the order parameter. The studies on the dynamics of the liquid crystal director for sample spinning near magic angle in mesophases with positive and negative diamagnetic susceptibility anisotropies (Delta chi) and their mixtures with near-zero macroscopic diamagnetic susceptibility anisotropies have been reported. In systems with weakly positive Delta chi, the director has been observed to switch from an orientation parallel to the spinning axis at low rotational speeds to one perpendicular to the spinning axis at high rotational speeds, when the angle theta, the axis of rotation makes with the magnetic field is smaller than the magic angle theta(m). For systems with a small negative Delta chi, similar director behaviour has been observed for theta greater than theta(m). At magic angle, the spectra under slow spinning speeds exhibit a centre band and side bands at integral values of the spinning speeds. The intensities of the spinning side bands have been shown to contain information on the sign and the magnitude of the order parameter(s). The results are discussed with illustrative examples. Results on the orientation of the chemical shielding tensor obtained from a combination of the NMR studies in the solid and the liquid crystalline states, have been described.