Consciousness is generally considered to emerge from synaptic computation among brain neurons, but this approach cannot account for its critical features. The Penrose-Hameroff “Orch OR” model suggests that consciousness is a sequence of quantum computations in microtubules within brain neurons, shielded from decoherence to reach threshold for objective reduction (OR), the Penrose quantum gravity solution to the measurement problem. The quantum computations are “orchestrated” by neuronal/synaptic inputs (hence “Orch OR”), and extend throughout cortex by tunneling through gap junctions. Each Orch OR is proposed as a conscious event, akin to Whitehead’s philosophical “occasion of experience”, occurring in concert with brain electrophysiology. This chapter discusses the need for such an approach and its neurobiological requirements.