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The study of solute transport in porous media continues to find applications in both traditional and emerging engineering problems, many of which occur in natural environments. Key applications include CO2 sequestration, enhanced oil recovery and soil remediation. Transport is a fundamental component in the analysis of these systems, because it provides the driving force for physical and chemical interactions between the fluid and the solid phase. However, the inherent heterogeneity of the subsurface leads to what is classically referred to as anomalous transport, which challenges classic interpretations of both field and laboratory experiments. In this context, novel laboratory protocols are needed to probe transport in heterogeneous medium by measuring the spatial structure of the concentration field in the medium, rather than relying exclusively on the analysis of breakthrough curves (BTCs). In this thesis, a combined experimental and modelling study of solute transport in a range of porous media has been presented, including sandstone and carbonate rocks, to cover a range of pore structures. At the core of the experimental work is the combination of two imaging methods, X-ray Computed Tomography and Positron Emission Tomography. While the former is used to characterise rock properties spatially, the latter allows visualising the temporal evolution of the full tracer plume within the medium in three dimensions. To this aim, a core-flooding system has been built to carry out pulse-tracer tests over a wide range of Péclet numbers (Pe=15-500) using brine- and radio-tracers. In addition to the experiments on the three rock samples (Bentheimer Sandstone, Ketton Limestone and Edwards Carbonate), control experiments on uniform beadpacks were carried out to verify the accuracy of the in-situ measurements. The experimental BTCs have been analysed in the framework of residence time distribution functions, which revealed mass transfer limitations in the microporous carbonates in the form of a characteristic flow-rate effect. Three transport models: the Advection Dispersion Equation (ADE), the Multi-Rate Mass Transfer (MRMT) and the Continuous Time Random Walk (CTRW) framework have been thoroughly evaluated with both the BTCs and the internal concentration profiles. It is shown that the ADE provides an accurate description of the results on the beadpack and the sandstone. The data on the carbonates are better described by the MRMT, which uses a fraction of stagnant, intra-granular pore space and an external fluid film resistance model to account for mass transfer between the flowing fluid and the porous particles. The CTRW theory, applied here for the first time to carbonate cores, provides a further improvement in describing the BTC, because of its ability to account for unresolved heterogeneities. In the application of the models, a distinction was made between parameters that are rocks-specific (e.g., the dispersivity) and those that depend on the flow rate, by treating the former as global fitting parameters in the optimisation routine. Accordingly, the obtained results provide a more consistent picture than what the current literature may suggest regarding the use of these models to the analysis of BTCs. The dataset obtained from the PET has been used to quantify the extent and rate of mixing in the different porous media. The 3-D images clearly reveal the presence of spreading caused by subcore-scale heterogeneities. To quantify their effects on the core-scale dispersion, various measures has been used, namely the dilution index (Π), the spreading length-scale (K) and the intensity of segregation (I). It was observed that the microporosity has a pronounced effect on mixing, thereby greatly accelerating the time scale to reach the asymptotic regime. Notably, both Π and K scale vary linearly with the square-root of time, indicating the suitability of a Fickian-based model to quantify macrodispersion. This observation suggests that the strength of heterogeneity in the rock samples investigated is moderate and that anomalous transport has evolved to normal behaviour on a length-scale O(l)∼10 cm (∼ length of the samples). In this context, to provide a more comprehensive picture of anomalous transport in laboratory rock samples, future studies should aim at increasing the spatial resolution of the measurement. Non-invasive, imaging tools such as PET are likely to go a long way in addressing this problem and provide significant opportunities to advance our understanding of miscible displacements in consolidated porous media, thus including those involving additional phenomena, such as adsorption and chemical reactions.