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The formation of the large-scale structure in the universe is one of the most important problems in modern cosmology. Interest in this area has been spurred by promising confluence of theoretical ideas and a rapidly increasing observational database. The primary focus of this talk is to develop a better understanding of the dynamics involved in forming the large-scale structure via gravitational instability. I will review one currently popular approach that consists in developing of approximate analytical of semi-analytical models describing the non-linear stages of gravitational instability. A highly successful example of this kind approximation is the Zel'dovich approximate non-linear solution which describes the evolution of density inhomogeneities in a dust-like medium. Cosmological applications of some approximations will be discussed.
