In this review we compiled recent advances concerning the cooperative motion in crowded soft matter systems. We tried to answer the question how to perform dynamic Monte Carlo simulations of dense macromolecular systems effectively. This problem is not simple due to the fact that the movement in such systems is strictly correlated which leads to cooperative phenomena. The influence of crowding was found interesting especially for two-dimensional cases, e.g., in membranes where the presence of macromolecules, proteins and cytoskeleton often changed the mean-square displacement as a function of the lag time and anomalous diffusion appeared. Simple models are frequently used to shed a light on molecular transport in biological systems. The emphasis was given to the Dynamic Lattice Liquid model. The latter model became a basis for a parallel algorithm that takes into account coincidences of elementary molecular motion attempts resulting in local cooperative structural transformations. The emphasis is put on influence of the model of molecular transport on the diffusion. The comparison to alternative approaches like single agent model was carried out.