We present the results of investigations of the influence of the confinement, interface, porous matrix structure, pore size and shape on the dynamic behavior of nematic liquid crystals (LC) dispersed in porous matrices with randomly oriented, interconnected pores (porous glasses) and parallel cylindrical pores (Anopore membranes) by photon correlation and dielectric spectroscopies. Investigations of LC in cylindrical pores together with studies in random porous matrices, makes it possible to separate the role of random structure and domain formation from the contributions due to existence of LC - solid pore wall interface and pure finite size effect in different relaxational processes. We suggest that slow relaxational process observed in photon correlation experiments is due to the formation of interfacial layers on the pore walls rather than due to the dynamics of domains.