Mines have been in use as an anti-starship weapon since at least the 2150s - Romulans were known to use cloaked minefields at this time, leading to one incident in which significant damage was inflicted on the NX-01 when it accidentally wandered into such a field.  Gravitic mines were in use during the 22nd century - the disabling of a civilian spacecraft by a gravitic mine formed a part of Starfleet's Kobyashi Maru test. 
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Today the antimatter mine is a simple, no-frills weapon designed to be used in large numbers in order to restrict or deny an area of space to enemy forces. One of the simplest forms of mine is the command model; this consists of a matter and antimatter charge held suspended in containment fields within a small case which also holds a communications mechanism. This type of mine would be deployed within the scan radius of a controlling vessel; the ship then monitors the area for the approach of enemy vessels, detonating a mine by remote control when an enemy vessel approached it. If a long duration minefield is required a sensor drone can take the place of the ship. The Enterprise-D used such a minefield to force the surrender of a Cardassian fleet in the McAllister Nebula in 2369.  In 2372 the Klingon Empire attempted to place a minefield around the Bajoran system to prevent the Federation reinforcements from reaching the system in the event of a Klingon invasion. The plan was only revealed when one of the mines exploded by accident, badly damaging a Klingon cruiser. 
More complex and effective mines are each fitted with their own sensor system. Although this makes the mines slightly more difficult to construct, such a minefield is not dependant on a single drone to run it and is hence more resistant to countermeasures.
The better mines are essentially tiny drone spacecraft, fitted with their own independent sensors and drive system, controlled by an artificial intelligence computer. The Federation Type 16 mine is an example of this type - it constantly surveys space around it to a radius of five light seconds, analysing anything which enters this zone and comparing it to a pre-programmed file of enemy vessel types. The entire minefield can be networked together, allowing them to share sensor information between them. If an enemy target enters the field the mines will determine which one has the best possible intercept solution; this mine will activate its micro impulse drive at the appropriate moment and track in on the target, detonating its warhead at the moment of closest approach. The Type 19 mine operates in a similar manner but the mines are fitted with a small warp engine to allow them to engage targets using warp drive. At this level the mine is essentially a photon torpedo capable of lying dormant for long periods.
The most recent development in Federation mine technology is the model developed by an engineering team on Deep Space Nine under Chief Miles O'Brien. Barely a metre in diameter this is one of the smallest mines in use by the Federation.  It contains a photonic charge equal to several hundred grenades rather than a matter/antimatter charge, along with a micro impulse system and sensor system capable of scanning out to a radius of two thousand kilometres. The limited range and destructive capability is more than offset by the use of both a cloaking device and a replicator system on the mines; when a target is detected the mines swarm it, overwhelming the defences. Once the target is destroyed the mines in that area can replicate replacements to quickly bring the field back up to strength. This type of minefield is exceptionally difficult to clear; the use of a cloaking system on the mines means that an enemy can never be sure that every mine has been destroyed in a weapons barrage. Should only a handful survive to destroy another target, hundreds or even thousands more mines are quickly replicated and the field can be back up to full strength within hours. Such a minefield was deployed at the Bajoran Wormhole to block access by Dominion forces, triggering the Federation-Dominion war.  The Dominion forces which captured DS9 at the outbreak of the war struggled several months to disable the minefield without success before finally managing it just before the station was retaken by allied forces.