We propose a computational modeling approach that explains the formation of a range of spatial cells like head direction cells, grid cells, border cells and place cells which are believed to play a pivotal role in the spatial navigation of an animal. Most existing models insert special symmetry conditions in the models in order to obtain such symmetries in the outcome; our models do not require such symmetry assumptions. Our modeling approach is embodied in two models: a simple one (Model #1) and a more detailed version (Model #2). In Model #1, velocity input is presented to a layer of Head Direction cells, with no special topology requirements, the outputs of which are presented to a layer of Path Integration neurons. A variety of spatially periodic responses resembling grid cells, are obtained using the Principal Components of Path Integration layer. In Model #2, the input consists of the locomotor rhythms from the four legs of a virtual animal. These rhythms are integrated into the phases of a layer of oscillatory neurons, whose outputs drive a layer of Head Direction cells. The Head Direction cells in turn drive a layer of Path Integration neurons, which in turn project to two successive layers of Lateral Anti Hebbian Networks (LAHN). Cells in the first LAHN resemble grid cells (with both hexagonal and square gridness), and border cells. Cells in the second LAHN exhibit place cell behaviour and a new cell type known as corner cell. Both grid cells and place cells exhibit phase precession in 1D and 2D spaces. The models outline the neural hierarchy necessary to obtain the complete range of spatial cell responses found in the hippocampal system.