Carbonate rocks are considered to be essential reservoirs for human development, but are known to be highly heterogeneous and difficult to fully characterize. To better understand carbonate systems, studying pore-scale is needed. For this purpose, three blocks of carbonate rocks (chalk, enthrocal limestone, and dolomite) were cored into 30 samples with diameters of 18 mm and lengths of 25 mm. They were characterized from pore to core scale with laboratory tools. These techniques, coupled with X-ray micro-tomography, enable us to quantify hydrodynamic properties (porosity, permeability), elastic and structural properties (by acoustic and electrical measurements), pore distribution (by centrifugation and calculations). The three rocks have similar properties to typical homogeneous carbonate rocks but have specific characteristics depending on the rock type. In the same rock family, sample properties are different and similarities were established between certain measured properties. For example, samples with the same hydrodynamic (porosity, permeability) and structural (formation factor, electrical tortuosity) characteristics may have different elastic properties, due to their cohesion, which itself depends on pore size distributions. Microstructure is understood as one of the essential properties of a rock and thus must be taken into account to better understand the initial characteristics of rocks.