Anti-surface warfare (ASUW or ASuW) is the branch of naval warfare concerned with the suppression of surface combatants. More generally, it is any weapons, sensors, or operations intended to attack or limit the effectiveness of an adversary's surface ships. Before the adoption of the submarine and naval aviation, all naval warfare was, of course, anti-surface warfare. The distinct concept of an ASuW capability therefore is post-WW2, and literature on the subject as a distinct discipline is inherently dominated by the dynamics of the Cold War.
Categories of ASUW 
ASUW can be divided into four categories based on the platform from which weapons are launched:
- Air (or aviation): Anti-surface warfare conducted by aircraft. Historically, this was conducting primarily through level- or dive-bombing and strafing runs (and in some cases by suicide (Kamikaze) attack). Today, air ASUW is generally conducted by stand-off attacks using air-launched cruise missiles (ALCM) or air-to-surface missiles (ASM).
- Surface: Anti-surface warfare conducted by warships. Warships can use torpedoes, guns, surface-to-surface missiles, or mines. UAVs represent an emerging technology. Asymmetric methods include the suicide boat.
- Submarine: Anti-surface warfare conducted by submarines. Historically, this was conducted using torpedoes and deck guns. More recently, the submarine-launched cruise missile (SLCM) has become a preferred anti-ship weapon, offering a significantly longer range.
- Shore/Space: Historically, this refers to shore bombardment from artillery and cannon. Today, coastal-launched cruise or ballistic missiles are considerably more common. Further, ground-controlled satellites may provide datum on fleet movements.
Following the results of the Battle of Taranto and the Battle of Midway, the primary combatant ship type was the CV or fleet carrier. After WW2, the ASuW concept primarily involved the multiple carrier battle-groups fielded by the US Navy, against which the Soviet Union designed specialized strategies that did not equate to a 1:1 match of designs.
Broadly speaking, military planners in the US after WW2 envisioned that a Warsaw Pact invasion of Western Europe would require a massive convoy effort to Europe to supply Allied forces in theatre. Against this necessity of logistical and combat support, the Soviet Union expanded its submarine fleet, which in the event of hostilities may have been sufficient to deny the supply of material to the theatre. As military strategists often design counter-strategies to meet the capabilities of the rival force, the Western then responded with the construction of SOSUS lines to track Soviet submarines.
From the air, Russian naval aviation had ASuW capabilities. The Tupolev Tu-16 Badger G was armed with anti-ship missiles, followed by the Tupolev Tu-22M Backfire supersonic maritime strike bomber. Even the prop-driven Tu-142, primarily designed for ASW warfare, could and was armed with antiship missiles.
Today, following the end of the Cold War, ASuW still involves asymmetries, which may for now be more pronounced.
Air ASuW 
After the development of reliable long-range guided missiles, Air ASuW was imagined to consist of a mass attack by high-speed jet aircraft launching sufficient number of missiles to overwhelm the anti-air defences of a fleet. Some commentators believed that this capability was consistently underestimated. Exocet strikes against the Royal Navy during the Falklands War resulted even in the adoption of 'Exocet' as a slang term for a 'sharp, devastating and surprising attack.' The USS Stark incident showed a medium-sized power could significantly damage a superpower's most advanced air-defense frigate, with the attack of a single plane on a single ship capable of inflicting heavy damage, let alone the scenario of a multi-ship flight.
Surface AsuW 
After the launch of "airplane-carrying heavy cruisers," it once against became possible for two fleet battle groups to engage in some sort of heavy fleet-on-fleet surface action. The fall of the Soviet Union has prevented the results of such an action's outcome, but given the dramatically revealed capability of Air ASuW weaponry, a simple "completely domination" NATO estimation would likely have been naive.
Submarine ASuW 
Undersea versus fleet action is commonly described as a "cat-and-mouse" game, where submarines seek to escape detection long enough to engage in a punishing strike against the much more valuable CV fleet groups. Early Soviet submarine designs could be heard "across the Atlantic," but by the late 80s, many advanced designs were approaching sound-output equivalent to a body of water the size of the sub. P-3 Orions or other ASW maritime patrol planes could deploy Magnetic Anomaly Detectors or disposable sonobuoys, against which the concept of a submarine firing a SAM was generally considered a poor trade-off (the revelation of the submarine's location was not generally considered worth the possible hit on a single plane). However, the concept of the submarine firing on the plane has been revived with Germany's 209-class diesel submarines.
Submarines seeking to engage in ASuW can also be targeted by other submarines, resulting in wholly undersea combat.
Shore/Space ASuW 
Shore-based assets may have provided the decisive edge in surface warriors, with constrains imposed by range of such assets. Furthermore, satellies controlled from ground stations could provide information on enemy fleet movements.
Post Cold-War 
In the post-Cold War error, UAVs and asymmetric threats such as the suicide boat are adding additional complexity to the ASuW discipline.