Multiphase flows are ubiquitous in nature and engineering applications. Numerical modeling of such flows becomes an important complement to experimental studies with the rapid development of computational science, while it faces some certain challenges owing to complex interfacial dynamics involving multiple space and time scales. Physically, the interfacial phenomenon can be recognized as a natural consequence of intermolecular interactions among fluid molecules. In this regard, the lattice Boltzmann method based on the kinetic theory enables to conveniently describe the intermolecular interactions, which makes it become a suitable and popular candidate for modelling and simulating multiphase flows. In this talk, we will introduce our recent advance on the lattice Boltzmann method for multiphase flows. Then the method is applied to some important applications, mainly including turbulent Rayleigh-Taylor instability between immiscible fluids and the microdroplets dynamics.