Carbonate rocks have a very complicated and heterogenous porous structure in comparison with sandstone reservoir rock. To understand the transport processes in any porous medium, we need to enhance our knowledge of the geometry and topology of the porous media. Therefore, in this work we present advances with different multi-scale imaging techniques to obtain 2D and 3D images from core-scale (1mm) using Medical CT scanning to pore scale (1- 10µm) using Confocal Laser Scanning Microscopy (CLSM) and Micro CT imaging. First, we have developed a novel technique of CLSM to obtain 2D images with a large field of view, which is advantageous for scanning heterogenous carbonate rocks. We have obtained statistical data about total, macro and micro-porosity from 2D large field of view CLSM images and have validated the results using mercury intrusion capillary pressure (MICP) data. Second, we have obtained initial results using our Medical CT scanner for spontaneous imbibition of water in carbonate cores and measured the water saturation as a function of time. Also we have observed and compared the capillary heterogeneity in a simple sandstone core with a heterogeneous carbonate core sample. Finally, we have obtained 3D pore scale images of carbonate samples using our Micro CT scanner at different resolutions. By using image processing techniques for different phase segmentations, we study the effect of resolution on the measured porosity and permeability using Lattice Boltzmann simulations and pore network models. This gives valuable information about pore-throat connection and pore-throat sizes. Finally, we correlate the data for porosity and permeability for different carbonate rock samples taken at different resolutions.