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Carbonate rocks are well-known to be tremendously heterogeneous. They mainly consist of component particles (from biological and non-biological origin) embedded in a lime-mud matrix and/or in a cement (composed of even smaller particles). The size, shape, density and spatial arrangement of those particles, alongside with natural fractures and cracks (although those are certainly not exclusive to carbonate rocks), define a microstructural pattern that is known to have a great influence on rock physical properties. Thus, to understand carbonate rock systems at large scales (formation, reservoir ...), geophysicists have to study them at the pore scale, hoping to resolve the so-called "upscalling" problem. With this in mind, unravelling and identifying the relations between physical properties and carbonate rock microstructures is paramount for a global comprehension of a carbonate rock system. Since the late nineties, several research groups and authors have worked on documenting and providing significant insights into the microstructural parameters controlling the physical response of several rock properties (porosity, permeability, electrical conductivity, elastic, seismic and mechanical properties ...) in carbonates. This article proposes a review of this specialized literature, from the early and recent contributions in rock physics, with emphasis on the recent studies on carbonate rocks from the Paris basin. • Rock physical properties are linked to many microstructural parameters. • Those parameters can interact at many different scales. • Early studies on those problems discussed the geological concepts of pore systems. • Recent work have shown that pore space must be defined using geometrical factors. • This concerns both elastic and transport properties in carbonate rocks. [ABSTRACT FROM AUTHOR]