In modern high resolution SAR data, due to the intrinsic side-looking geometry of SAR sensors, layover and foreshortening issues inevitably arise, especially in dense urban areas. SAR tomography provides a new way of overcoming these problems by exploiting the back-scattering property for each pixel. However, traditional non-parametric spectral estimators, e.g. Truncated Singular Value Decomposition (TSVD), are limited by their poor elevation resolution, which is not comparable to the azimuth and slant-range resolution. In this paper, the Compressive Sensing (CS) approach using Basis Pursuit (BP) and TWo-step Iterative Shrinkage/Thresholding (TWIST) are introduced. Experimental studies with real spotlight-mode TerraSAR-X dataset are carried out using both BP and TWIST, to demonstrate the merits of compressive sensing approaches in terms of robustness, computational efficiency, and super-resolution capability.