I posted my opinion on subs a while back, but I think nobody noticed, so here's a repost.
This is how I think they should work (long and boring

).
1) Regular submarines.
1.1) Submarine is normally visible to normal units.
1.2) Submarine is normally attackable by normal units.
1.3) Submarine recieves a "Mission: Torpedo Attack" button.
1.3.1) Mission: Torpedo Attack can be initiated in any square
1.3.2) When Mission: Torpedo Attack is initiated, submarine submerges, becoming invisible to normal units.
1.3.3) While performing Mission: Torpedo Attack, submarine's speed is lowered by 1 (number subject to tweaking).
1.3.4) After submerging, submarine automatically attempts to intercept target and inflict a strong bombardment-type attack on it.
1.3.5) After attack, submarine automatically attempts to get away from any enemy units for as far as it can before it is forced to surface.
1.3.6) Maximum range while submerged is 10 squares (number subject to tweaking)
1.4) Submarine can also engage targets without initiating torpedo attack. In this case, it functions as a surface ship, with attack/defense of 4/4 (number subject to tweaking). This mode is mainly for attacking "soft" targets, like unescorted transports or obsolete ships, and simulates cannon firing instead of launching torpedos.
2) Nuclear submarine.
2.1) Nuclear submarine is in constant, controllable Mission: Torpedo Attack mode.
3) Anti-Submarine Warfare (ASW).
3.1) Detecting submerged submarines.
3.1.1) Passive detection.
3.1.1.1) When a submerged submarine moves or attacks within a detection range of a Destroyer or AEGIS Cruiser, it has a chance of being revealed. Chance is cumulative for multiple detecting ships.
3.1.1.2) Destroyer has a detection range of 2 squares, and chance of 10% (numbers subject to tweaking)
3.1.1.3) AEGIS Cruiser has a detection range of 3 squares, and chance of 15% (numbers subject to tweaking)
3.1.2) Active detection.
3.1.2.1) Destroyer and AEGIS Cruiser recieve a Mission: ASW button.
3.1.2.2) When conducting Mission: ASW, ships are unable to move.
3.1.2.3) Mission: ASW raises detection chance 10% (number subject to tweaking).
3.2) Destroying submerging submarines.
3.2.1) Destroyers and AEGIS Cruisers are capable of attacking detected submarines.
3.2.2) While conducting Mission: ASW, they do so automatically.
3.2.3) Aircraft are capable of attacking submerged submarines with Mission: Precision Strike.
I believe this should cover it Basically, submarine becomes a sorta-underwater-bomber, while destroyers and AEGIS cruisers can perform interceptor duties. Attacking a fleet covered with an ASW screen is sorta suicidal, but unescorted battleships and carriers are meat

Aircraft hitting subs with precision strike simulates them using air-launched depth charges and torpedoes.