Why does a submarine not implode under water?

Submarines will implode very well if they go to a depth past their rated crush depth.

All boats are designed to withstand a lot of PSI on the hull, and most boats are designed so that the hull contracts and expands with depth changes. This ability to flex increases the longevity of the hull, though not all navies build their boats that way.

In addition to hull design (usually spherical or cigar shaped, the best design for pressure), boats maintain a positive air pressure inside while submerged. This is less about pressure on the hull than it is to maintain a vigil on hull integrity; if pressure in the boat drops, it means there's a leak or flooding somewhere, or a hatch not sealed properly.