In quantum physics, there's a small chance that my hand will suddenly pass through the table. But it's phenomenally unlikely, because my hand is quite large. For tiny objects, tunnelling happens all the time. In fact, if tunnelling didn't happen, the sun would not shine. Tunnelling is not more strange than the rest or unexplained than the rest of quantum physics. So if you can get a good picture of the world that comes with quantum physics, you get tunnelling for free.