Russian special purpose regiments or Spetsnaz, Specnaz (Войска специального назначения - спецназ/Voyska spetsialnogo naznacheniya, /spʲeʦnaz/ in IPA) is a general term for "special forces" in Russian, literally "special purpose units".
In Russian the term commonly denotes the special forces of all countries and is used by mass media, and civil people to mark all kinds of special purpose units of all kinds of subordination; in English it refers exclusively to the Russian special forces.
In fact, its use in English usually is associated with Russians writing in English or with writers attempting linguistic authenticity. Generally, English-language media refer to them as "Russian special forces".
Spetsnaz can refer to any elite or special purpose units controlled by the Federal Security Service (FSB) with counter-terrorist and anti-sabotage tasks, Ministry of Interior (police) MVD, and the army special forces controlled by the military intelligence service GRU. Nowadays, the term is used as well to describe any special purpose units or task forces of other ministries (even the Emergency Situations Ministry special rescue unit).
Strictly speaking, all Spetsnaz units operated by the KGB/FSB were called OSNAZ, an acronym for [voiska] osobogo naznacheniya or "special purpose [detachments]". These units originally were raised for internal use against right-wing counter-revolutionaries, dissidents, and other undesirables. There has always been a certain amount of shifting of personnel and units between both the GRU who control SPETSNAZ and the MVD with OSNAZ MVD and OSNAZ KGB or FSB, especially between the latter two. Today, OSNAZ is a term mainly used in connection with GRU-controlled COMINT, ELINT and radio-surveillance units within the Armed Forces.
Spetsnaz carry out reconnaissance and social warfare missions in "peacetime" as well as in war. For example, it is known that the assassination of Afghanistan's president carried out by Spetsnaz in December 1979 was under the direction of the KGB.
According to Vladimir Rezun, a GRU defector who used the pseudonym "Viktor Suvorov", there were 20 Spetsnaz brigades plus 41 separate companies. Thus, total strength of Spetsnaz forces in the 1980s could have been around 30,000 troops.

Ministry of Interior units
"Nobody but us. Rossiyskiy specnaz."
Spetsnaz GRU, or Russian army special forces, are the original SPETSNAZ and are generally considered the best trained units of the Armed Forces of the Russian Federation. Despite this, they are not very similar to the Special Forces of the US or the SAS of the UK. The Spetsnaz have created a fierce reputation as one of the best special forces in the world today due to the very harsh standards of their training. They are controlled by the GRU (the Russian military intelligence agency). During the Cold War, these units were deployed in Eastern Europe in order to carry out reconnaissance and sabotage missions against the NATO forces in the event of a war in Europe. The units of Spetsnaz GRU have no official names, such as is the case with units of Spetsnaz MVD. They are generally referred to by numbers, for example, "16th Separate Brigade of Spetsnaz", much like any other military unit, and are usually integrated in the structure of the VDV (airborne troops) though not under VDV command aegis.
Few details are actually known about the operations of Spetsnaz GRU, but it is known that the units were heavily involved in wars in Afghanistan and Chechnya. Spetnaz GRU teams usually wear standard-issue VDV uniforms, light blue VDV berets and unit patches in order to avoid identification. However, they can also wear different uniforms, for instance, they would wear the uniform of a unit which is stationed nearby, in order to blend in.
Here are most of the Spetsnaz Brigades and the location at which they are stationed:
and many others, including:
A Spetsnaz brigade consists of three to five Spetsnaz battalions, a signals company, support units, and a headquarters company containing highly skilled professional soldiers responsible for carrying out assassinations, kidnappings, and contact with agents in the enemy rear area. The organisation of a naval SPETSNAZ brigade reflects its emphasis on sea infiltration, with up to three frogman battalions, one parachute battalion, and a mini-submarine battalion, as well as the signals company, headquarters company, and support elements.

2nd ObrSpN - Promezhitsy (Pskov region); strength around 960 (Leningrad Military District)
3rd Guards ObrSpN - Roshinskij (Samara Oblast); (Volga-Ural Military District)
10th (Mountain) ObrSpN - Molkino (Krasnodar region); activated July 1, 2003 (North Caucasus Military District)
12th ObrSpN - city of Asbest-5 Sverdlovsk region); (Volga-Ural Military District)transferring: Chaikovskyy (Perm')
22nd Guards ObrSpN - Kovalevka (Rostov Oblast); (North Caucasus Military District)
67th ObrSpN - Berdsk (Novosibirsk Oblast); (Siberian Military District)
83 SPETZNAZ CDO BDE Ussuryysk (Far East Military District)
216 INDEP SPETZNAZ BN Moscow (Moscow Military District)
14th Separate Brigade of Special Designation Ussuriysk, Far Eastern Military District
16th Spetsnaz Brigade - formerly Teplyi Stan, suburb of Moscow, now [Tambov[Chuchkovo]], Moscow Military District
24th Spetsnaz Brigade - [Ulan-Ude[Kyakhta]], Siberian Military District Russian army special forces
The Soviet Naval Spetsnaz came in to being in 1957 by order of Defence Minister Zhukov.The Black Sea fleet created their spetsnaz unit in 1967. A marine counter terrorist and counter sabotage unit was created in 1969 as "protivodiversionniye sili i sredstva"-counter-underwater forces. In 1970, the Main intelligence service of a General staff (GRU) created a top secret reconnaissance - sabotage group "Delfin" (Dolphin) for operations against sea bases of foreign states. Instructors from group "Delfin" prepared the combat swimmers for KGB groups "Alfa" and "Vympel". At the fall of the Soviet government, each of the Soviet Red Banner Fleets (four total) had a Naval Spetsnaz Brigade assigned to it (see combat swimmers). Furthermore, modern Alfa and Vympel special purpose forces also have naval units.
Russian Naval Infantry, or the Russian Marines, are elite forces, but by no means are they Spetsnaz troops as Naval Special Operations would be carried out by Delfin (Naval Spetsnaz) troops rather than the Marines, which are intended to spearhead amphibious invasions. The 4 Major Naval Spetsnaz units are:

4 INDEP SPETZNAZ PT Parusnoe (Baltyysk) (Baltic Fleet) formerly Viljandi, Estonia (transferred from Army GRU to Navy GRU)
431 INT SPETZNAZ PT Tuapse (Black Sea Fleet) formerly Kronstadt (Baltic Fleet)
42 SPETZNAZ PT Russkyy island (Pacific Fleet)
420 INT SPETZNAZ PT Polyarnyy (Northern Fleet) Russian Naval Spetsnaz
Russian intelligence agencies, MVD, FSB, and the FPS and the Foreign Intelligence Service (SVR, "Sluzhba Vneshnej Razvedki", Russian equivalent of the American CIA) have their own Osnaz units.

The use of the term in the Russian language as of 2004

Alpha Group
Vympel
Rus (special forces)
Vityaz (MVD)
OMON
SOBR
VDV
Spetsnaz (miniseries)