Spatial cells in the hippocampal complex play a pivotal role in the navigation of an animal. Exact neural principles behind these spatial cell responses have not been completely unraveled yet. Here we present two models for spatial cells, namely the Velocity Driven Oscillatory Network (VDON) and Locomotor Driven Oscillatory Network. Both models have basically three stages in common such as direction encoding stage, path integration (PI) stage, and a stage of unsupervised learning of PI values. In the first model, the following three stages are implemented: head direction layer, frequency modulation by a layer of oscillatory neurons, and an unsupervised stage that extracts the principal components from the oscillator outputs. In the second model, a refined version of the first model, the stages are extraction of velocity representation from the locomotor input, frequency modulation by a layer of oscillators, and two cascaded unsupervised stages consisting of the lateral anti-hebbian network. The principal component stage of VDON exhibits grid cell-like spatially periodic responses including hexagonal firing fields. Locomotor Driven Oscillatory Network shows the emergence of spatially periodic grid cells and periodically active border-like cells in its lower layer; place cell responses are found in its higher layer. This model shows the inheritance of phase precession from grid cell to place cell in both one- and two-dimensional spaces. It also shows a novel result on the influence of locomotion rhythms on the grid cell activity. The study thus presents a comprehensive, unifying hierarchical model for hippocampal spatial cells. © 2018 Federation of European Neuroscience Societies and John Wiley & Sons Ltd