Recent progress in experiments including single molecule experiments revealed unexpectedly that various materials and biological systems are in non-equilibrium state. For example, the conformational relaxation of a DNA in a viral capsid is so slow that the relaxation time is comparable to the lifetime of the viral capsid. In other words, the viral capsid would spend its whole life in non-equilibrium state. As another example for materials systems, polymer nanocomposites, a mixture of polymers and nanoparticles, are usually not dispersed well with agglomerates of nanoparticles. The agglomerates of nanoparticles are often kinetically frozen, which hinders the materials from approaching the equilibrium state. Even though many systems of great interest are in non-equilibrium state, we do not yet have both solid theoretical foundations and simulation methods to understand what would happen in non-equilibrium state. And there are many unanswered yet old questions including the reaction kinetics and abnormal transport properties in non-equilibrium state. In this talk, I will discuss a few simulation studies that my research group performed to tackle such questions: (1) the loop formation kinetics of a single polymer in supercooled liquids, (2) the lipid transport in the liquid ordered phase of lipid bilayers and (3) the dynamics of polymers and colloids in confinements.