Modern submarines are quiet. Very quiet. Especially diesel-electric propelled submarines.
That makes them hard to find. Very hard.
Like black holes, modern submarines can often be detected indirectly; that is not by direct observation, but detecting their interactions with their underwater environment.
A surface ship searching for a submarine needs to balance its need to maintain its own stealth while seeking a tactical advantage when deciding to use passive sonar (listening only), or active sonar (transmitting an acoustic ‘ping’).
Passive sonars are currently hard-pressed to hear a submerged submarine, operating deliberately quietly, beyond 1000 yards (about one kilometre); the volume of background, ambient ocean noise quickly exceeds the volume the submarine, itself, is operating at. After 1000 yards, a submarine basically disappears into the background of noise created by whales, weather, and other man-made noises.
Active sonars take the advantage of transmitting noise, and listening for echoes as the signal reflects off a solid object within the water. Achievable ranges vary with the propagation conditions of the water: basically, how hot/salty/deep is the water. Acoustic physics for both passive and active sonar is interesting, and challenging. While an active ping might detect an otherwise-hidden submarine, the ship transmitting the ping has shown its cards. If the submarine was unaware of the ship’s presence before the ping, it is certainly aware of it after the event.
Anti-submarine warfare is about trade-off: environmental knowledge to predict sonar performance (predominantly), versus proactive submarine hunting, versus the need for ship quietness, versus the anti-submarine warfare mission, versus the overall mission. That’s why ships like to make heavy use of maritime patrol aircraft and helicopters. Aircraft offer tactical flexibility, another array of acoustic sensors that can be quickly deployed/re-deployed, and offer the submarine a nuisance to contend with if it knows it has already been discovered by another ship or aircraft.
Submarine v submarine warfare is a knife-fight in the dark, fought by the blind. Whoever gets to shiv the other one first is likely to win the contest, or have first rights to escaping the scene. The stakes are extraordinarily high for everyone concerned, even for those standing-off watching (listening) to events unfold.
Unless you have proof a submarine is in a given area (with increasing gradings of confidence based on evidence present at a given time), you might be fighting, or preparing to fight, a large marine mammal (aka a whale).
Which brings us back to the start: modern submarines are very quiet, and very hard to find.
So when an already successful submarine type is improved, professional submarine hunters should be demanding improved combat systems, doubling-down on tactical development and committing to practicing a difficult art of naval warfare.
This link: http://nationalinterest.org/blog/the-kilo-class-submarine-why-russias-enemies-fear-the-black-18140 gives an excellent top-level insight into the history and basic evolution of the Kilo-class submarine and its use around the world. It should offer ASW Officers and airborne tacticians cause for concern.