This thesis focuses primary on two-phase displacements under capillary-controlled flow conditions at relatively large scales, considering solution techniques that capture the dynamics of two-phase displacements for homogeneous flow domains, and deriving representative averages for heterogeneous systems with strong spacial variations in two-phase properties. First, we review main flow mechanisms encountered at large scales when capillary forces dominate the displacement process, where we present main solution techniques for homogeneous flow domains and introduce analytical treatments for other flow mechanisms that do not follow standard time-scaling. We also present a comprehensive investigation of spontaneous imbibition processes in porous rocks both numerically and analytically, and propose a simplified but accurate analytic approximation using perturbation theory, that considerably improves the implementation process, as compared with the original analytical solution. After that, an investigation of the impact of capillary backpressure on counter-current flow is performed, as this is considered one of the main drawbacks in using the continuum modelling approach. We then apply steady-state capillary-controlled upscaling in heterogeneous environment, where large-scale invasion percolation is coupled with a conventional Darcy solver to identify large-scale trapping due to capillary forces. In other words, a phase may fail to form a connected path across a given domain at capillary equilibrium, and some regions therefore may produce disconnected clusters. In such cases, conventional upscaling processes might not be accurate since identification and removal of these isolated clusters are extremely important to the global connectivity of the system and the stability of the numerical solvers. We present a comprehensive investigation using random absolute permeability fields, for water-wet, oil-wet and mixed-wet systems, where we show that in oil-wet and mixed-wet media, large-scale trapping of oil controlled by variations in local capillary pressure, may be more significant than the local trapping controlled by pore-scale displacement.