We developed an integrative spiking neuron framework to study motor learning and control across multiple levels of biological organisations from synaptic learning rules via neural populations and muscles to an arm's movements. Our framework is designed to simulate reward-based motor learning processes by using identified cellular learning mechanisms (neuromodulation) and enable linking these to findings in human and primate motor learning experiments involving reaching movements. The key learning mechanisms are Actor/Critic reward-based learning and STDP synaptic plasticity rules. We simulate and study learning of planar reaching movements, where motor neuron activities drive Hill-type muscle models which mechanically translate forces into movements via a physics simulator. Our simulated brain is trained and tested in a reaching task with unknown dynamics following a psychophysics protocol. The framework is capable of learning the task and we can directly access the output of neuronal populations (e.g. M1, S1, VTA) as well as EMG-equivalent muscle activations, arm reaching trajectories and sensory feedback before, during and after motor learning. Our ability to simulate and explain motor learning across the levels of neural activity as well as psychophysics experiments will be useful in linking human motor learning experiments to their neuronal correlates. This system can thus provide incisive in silico proof-of-principle tests for understanding invasive approaches Brain-Computer-Interfaces and Neuroprosthetics.