Sometimes, a directed particle beam isn't enough. You want to cause some serious hurting and you're in a place where firing a concentrated stream of second-stage electrons is bad news. Or you're in space and you need to dump off some destructive power and high-tail it before your engines explode. Now is the time to bring an actual, mechanical weapon into play. Welcome to the old school. It's time for torpedoes.
A spatial torpedo is a tried and true weapon against unshielded structures. In the 21st and 22nd centuries, these were the primary armament of spacecraft, along with a hard-1S-radiation laser assembly. A spatial torpedo is little more than an old-fashioned first-stage fusion explosive, usually a large quantity of hafnium with a selectable-load x-ray emitter surrounding it. With no real guidance mechanism aboard, no shielding, and slow thrust, these outdated units see little use except cracking small asteroids for mining operations.
A photon torpedo (named in the 22nd century, apparently an orphaned injoke from testing labs) boils down to about half a starship's warp engine. Specifically, the half that blows up if treated improperly. A photon torpedo consists of little more than a pair of matter and antimatter bottles surrounded by some simple magnetic constriction elements, with a sliver of dilithium between the constrictors to generate power. When the detonator is triggered, the magnetics are deactivated and the matter and antimatter mix freely, generating a tremendous explosion. These devices are typically powered by a warp "sustainer engine", which permits travel at the ship's current Warp speed by bleeding off a portion of the vessel's larger subspace field. Sublight motive power is provided through a very small impulse engine. There is just enough dilithium to operate a torpedo's engine and power systems for an hour before detonation.
The quantum torpedo is what happens when the Starfleet Corps of Engineers decides that they need a multi-gigaton explosive device that can be loaded and fired from existing equipment. It is the evolution of a failed engine design first tested in 2356, a method for extracting zero-point energy from a Genus-1 topology string in an ultraclean vacuum. Unfortunately, this system is incompatible with the universe's functioning, making the quantum torpedo, when active, violently allergic to existing in a non-exploded state. Under a persistent subspace field generated by a small sarium-crellide battery-operated generator, a quantum torpedo can remain active and stable for almost a half hour. Once the field is released, either by the battery's expiration, detonation trigger, or damage to the unit the payload's total potential energy is released violently in an explosion of many times the magnitude that a photon torpedo generates.
The Romulans took a page from the Federation's books on this one. A compressor torpedo, sometimes called a gravity torpedo, is centered around a metastable artificial quantum singularity that provides power to the entire unit. Much smaller and "lighter" when stored than a photon or quantum torpedo, the compressor also has the significant advantages borne out in the quantum torpedo's design, only in a stable form. It has a vast storehouse of energy, and does not require a sustainer drive, able to operate for upwards of several days without losing power. Once initialized, an artificially-generated quantum singularity is generated in the torpedo's engine core. On detonation, that singularity is exposed to vacuum and permitted to flourish momentarily as a very small and short-lived but otherwise fully-fledged black hole. Strikes from a comp torpedo make the stricken object appear 'stretched' at the point of impact, and they leave a lot of first-stage radiation leaking about.
The Borg have assimilated many things. Worlds, peoples, spacecraft. And this torpedo simplifies things greatly for them. Like the others, it is a missile that is fired from a spacecraft when particle beams would not achieve the desired effect. The Projectile System 953 12•R7/E, Federation designation "constructor torpedo" achieves a different desired effect than the others, and is not simply based on the principle of overloading a tiny engine. Instead, a constructor torpedo is a densely-packed set of machinery. Upon transpenetrating an enemy's hull, the constructor torpedo rapidly breaks apart into biomechanical components of varying size and purpose, mostly constructed from nonsentient pests aboard previously-assimilated spacecraft, or modified viruses in the case of nano-scale machinery. These components then begin to infiltrate ship's systems, installing Borg technology as they proceed. Slowly, they begin to assimilate the craft and its crew from the inside out and, unless stopped, bringing a new ship into the collective swiftly and (relatively) easily.
The traditional missile weapon of the Klingon Empire. Where other cultures busy themselves with tiny collapsing engines or vermin that breach and infiltrate, the Klingons take combat more... personally. An Impact Torpedo is little more than a shield-breaching system, a device intended to slam into the protective fields of an enemy spacecraft at high speeds, using a small yet potent array of sensors to analyze the frequency of the defenses before it is vaporized. Once the target's shield frequencies are known, it is simple enough for the Klingons to calibrate their transporters and flick boarding parties over to the enemy vessel. It is worthy of note that the torpedo more frequently breaks up than successfully transmits any shield frequencies, and when it is able to transmit, countering the inbound wave of boarding parties is as simple as rotating the shield frequencies. It is for this precise reason that the torpedoes are small, relatively light, and use only a Warp sustainer and a primitive rocket engine to power themselves. A Bird of Prey can carry and fire several hundred Impact Torpedoes.