The mammalian neocortex possesses the remarkable ability to translate complex sensory inputs into abstract representations through the coordinated activity of large neuronal ensembles across the sensory hierarchy. Theoretical works have proposed a variety of algorithms to coordinate learning across this hierarchy, including approximations of backpropagation of error as well as target-based methods such as predictive coding or control methods. In order to test the biological validity of these algorithms, we analyze the learning principles of the cortex, starting at the level of the synapse and working up toward network learning. We begin by adopting a calcium-dependent synaptic plasticity rule consistent with a wide range of molecular and electrophysiological findings and implement this rule in a synaptic model. We then embed our synaptic model into a pyramidal neuron model with apical and dendritic compartments, and integrate various experimental observations such as somato-apical coupling, calcium plateaus, and BAC firing. Our model predicts that apical inputs guide basal plasticity through sustained membrane depolarization and cause increased firing rates, and we validate these predictions with ex vivo electrophysiology experiments on layer 5 pyramidal neurons from the mouse prefrontal cortex. We evaluate the learning principles of backpropagation of error and target learning by building networks of our neuron model that receive learning signals at the apical dendrite. We contrast our network simulations with calcium imaging recordings, and find that the neuronal activities produced by target learning align with population activities observed in the cortex before and during spontaneous reactivations, whereas those from backpropagation do not. Taken together, our theoretical work corroborated by our biological data and network simulations provide evidence in favor of target learning and against backpropagation of error and its variants as the learning principle of the mammalian neocortex.