Oil companies aim to increase their return on investment by extending the productive life of their existing oilfields. For that purpose, a better understanding of the physical phenomena which occur during waterflooding and enhanced oil recovery (EOR) is needed to optimise the oil recovery. In this thesis, Nuclear Magnetic Resonance (NMR) has been employed to detect fluid displacement at reservoir-representative velocities and dynamically monitor the oil and water behaviour during brine and polymer core flooding. The first step for the analysis of the physical phenomena was the detection of velocities lower than 10 ft d-1 using Magnetic Resonance Imaging (MRI). For that reason, an optimisation toolbox, which uses the relaxation times and the diffusion coefficients of the porous system as input and derives the optimum experimental parameters for the MRI sequence, was developed. The novel MRI technique, also known as phase-contrast imaging, was initially tested in the ideal system of a bead pack having pore-scale resolution. Water velocities as low as 1 ft d-1 (3.5 μm s-1) were detected for the first time. The acquisition of velocity maps in less than 1 h was achieved by taking advantage of the novel method for under-sampling of the k-space. The parameters of compressed-sensing reconstruction were optimised giving results of high quality. Combining the velocity maps with 3D spatially-resolved propagators without pore-scale resolution enabled the identification of the mechanisms of mechanical and diffusive mixing along the sample. Phase-contrast imaging and 3D spatially-resolved propagators were also employed for the detection of ultra-slow flows through one sandstone and three low-permeability carbonate core plugs. Interesting observations were derived for flow velocities below 15 ft d-1 in these complex pore structures. After detecting ultra-slow flows through rocks, the research focused on the study of two-phase systems. A novel MRI sequence which enables the acquisition of 3D spatially-resolved propagators for the water and oil phase separately was developed and was tested in a bead pack and a carbonate rock. Then, oil was injected into a carbonate rock until the system reached reservoir-representative oil saturation. One-dimensional NMR spectra were used to monitor the saturation profiles, showing that water-wetting layers were distributed uniformly along the core. Brine was injected into the system simulating the process of waterflooding. The brine injection was monitored with chemically-selective images acquired in 16 min for each phase. The invasion percolation with cluster growth was identified as the main mechanism of oil displacement and 55.2% of the Original Oil In Place (OOIP) was removed. Then, brine injection was abruptly increased removing another 4.6% of OOIP trapped in the form of oil ganglia. The rest of the oil was trapped in unswept areas of the rock which could not be accessed by the abrupt increase in the brine injection. Xanthan gum polymer-EOR flood was employed to extract oil from these unswept areas. Comparison between the chemically-selective images and spatially-resolved propagators acquired before and after the polymer injection showed the diversion of the brine flow paths. This behaviour of the brine propagators was related to the blocking of the pores and throats due to the deposition of polymeric molecules as mentioned in the literature. An extra 8.5% of OOIP was removed during the consecutive polymer and brine injections. Moreover, interesting insights into the different flow behaviour of the brine and the polymer were obtained by comparing the propagators of each phase obtained under the same conditions.