Life on Earth can be traced back to as far as 3.8 billion years (Ga) ago. The catastrophic meteoritic bombardment ended between 4.2 and 3.9 Ga ago. Therefore, if life emerged, and we know it did, it must have emerged from nothingness in less than 400 million years. The most recent scenarios of Earth accretion predict some very unstable physico-chemical conditions at the surface of Earth, which, in such a short time period, would impede the emergence of life from a proto-biotic soup. A possible alternative would be that life originated in the depth of the proto-ocean of the Hadean Earth, under high hydrostatic pressure. The large body of water would filter harmful radiation and buffer physico-chemical variations, and therefore would provide a more stable radiation-free environment for pre-biotic chemistry. After a short introduction to Earth history, the current tutorial review presents biological and physico-chemical arguments in support of high-pressure origin for life on Earth.