Brain function relies on circuits of spiking neurons with synapses playing the key role of merging transmission with memory storage and processing. Electronics has made important advances to emulate neurons and synapses and brain-computer interfacing concepts that interlink brain and brain-inspired devices are beginning to materialise. We report on memristive links between brain and silicon spiking neurons that emulate transmission and plasticity properties of real synapses. A memristor paired with a metal-thin film titanium oxide microelectrode connects a silicon neuron to a neuron of the rat hippocampus. Memristive plasticity accounts for modulation of connection strength, while transmission is mediated by weighted stimuli through the thin film oxide leading to responses that resemble excitatory postsynaptic potentials. The reverse brain-to-silicon link is established through a microelectrode-memristor pair. On these bases, we demonstrate a three-neuron brain-silicon network where memristive synapses undergo long-term potentiation or depression driven by neuronal firing rates.