During the exploration of novel environments, place fields are rapidly formed in hippocampal CA1 neurons. Place cell firing rate increases in early stages of exploration of novel environments but returns to baseline levels in familiar environments. Although similar in amplitude and width, place fields in familiar environments are more stable than in novel environments. We propose a computational model of the hippocampal CA1 network, which describes the formation, dynamics and stabilization of place fields. We show that although somatic disinhibition is sufficient to form place fields, dendritic inhibition along with synaptic plasticity is necessary for place field stabilization. Our model suggests that place cell stability can be attributed to strong excitatory synaptic weights and strong dendritic inhibition. We show that the interplay between somatic and dendritic inhibition balances the increased excitatory weights, such that place cells return to their baseline firing rate after exploration. Our model suggests that different types of interneurons are essential to unravel the mechanisms underlying place field plasticity. Finally, we predict that artificially induced dendritic events can shift place fields even after place field stabilization.