This thesis focuses on the lattice-Boltzmann method (LBM) and its ability to simulate immiscible two-phase flow. We introduce the main lattice-Boltzmann-based approaches for analyzing two-phase flow: the color-fluid model by Gunstensen, the interparticle-potential model by Shan and Chen, the free-energy model by Swift and Orlandini, and the mean-field model by He. The first objective is to assess the ability of these methods to maintain continuity at the interface of two fluids, especially when the two fluids have different viscosities or densities. Continuity issues have been mentioned in the literature but have never been quantified. This study presents a critical comparison of the four lattice-Boltzmann-based approaches for analyzing two-phase flow by analyzing the results of the two-phase Poiseuille flow for different viscosity ratios and density ratios. The second objective is to present the capability of the most recent version of the color-fluid model for simulating 3D flows. This model allows direct control over the surface tension at the interface. We demonstrate the ability of this model to simulate surface tension effects at the interface (Laplace bubble test), stratified two-phase flows Poiseuille two-phase flow), and bubble dynamics (the free rise of a bubble in a quiescent viscous fluid).