Military police
The Life Guards are also the seat of the Swedish military police unit (MP-enheten) which is responsible for the education of new MPs and is in charge of all MP activities in Sweden. Part of 13th security battalion, which is a counter-intelligence battalion, is also part of the Life Guards and has some soldiers who are trained MPs (mostly corporals and sergeants).

Switzerland: In the Swiss Armed Forces, the Military Police is responsible for law enforcement on military property and for all incidents where military personnel or equipment is involved. Unlike, for example, the United States, a military policeman in Switzerland has the same power to arrest any person that has committed an offense he witnessed or if he has reasonable grounds to believe the person has committed a violent offense.
Furthermore, the military police provides protection of Swiss representatives abroad and is in part responsible for the guarding of embassies and foreign VIPs in Switzerland, as well as maintaining personal security for members of the Swiss Federal Council. In addition, the Swiss Explosive Ordnance Disposal Center is a branch of the MP for the disposal of unexploded ordnance and also participates in various demining operations around the world.
The professional MP units comprise 758 officers and are divided into four Regions, each consisting of two companies and additional groups specialised on criminal investigations and training. The professional MP maintains a standing tactical team, capable of interventions in Switzerland and abroad, headquartered in Bern. In addition, there are four militia MP battalions with a head count of roughly 2000 men. Each MP Battalion has one tactical company who can be called to support either the primary MP tactical team or cantonal police teams if needed.
Unlike regular army personnel, professional military policemen wear olive uniforms in order to provide distinct identification. Militia MP wear the regular Swiss Army TAZ 90 camouflage. Moreover, the (both the professional and the militia) MP is equipped uniquely, armed with Glock side arms, H&K MP5 submachine guns, the Mzgw91 pump-action rifle and the SG553 assault rifle (compared to the standard issue SIG P220 pistol and SIG 550 assault rifle). Professional MP units drive patrol cars similar to those of the civilian police, but also use Piranha and Duro APCs.

Ukraine: The Ukrainian Military Police (VSP) is the military police for the Ukrainian Armed Forces

United Kingdom: In the United Kingdom the term Military Police usually refers to the Royal Military Police. The Royal Military Police is the branch of the Adjutant General's Corps, responsible for policing the British Army (both in the United Kingdom and overseas). The term Service Police refers to the three separate police organisations for each of the three branches of the UK's Armed Forces:

The Royal Navy is policed by the Royal Navy Police (RNP), the members of which are traditionally known as Regulators (or Master-at-Arms if a Chief Petty Officer or Warrant Officer).
The Royal Navy Police also provides Royal Marines specialising as service policemen. Prior to 2009, the Royal Marines Police was an independent organisation.
The British Army is policed by the Royal Military Police (RMP).
In addition to the Royal Military Police, most British Army units have their own Regimental police (RP) and Military Provost Guard Service (MPGS) staff. Sometimes incorrectly referred to as Regimental Police, they do not have any police powers or policing function, but are soldiers responsible for discipline within their own units. They are normally located in the Guardroom.
The Royal Air Force is policed by the Royal Air Force Police (RAFP). The RAFP provides not only a full Policing function, but they also fulfil a security and counter intelligence function for the RAF and the wider defence community.
In addition, each of the three service police has its own Special Investigation Branch (SIB) to undertake investigation of more serious crime and plain-clothes investigations, and use the joint Service Police Crime Bureau operated by the RNP, RMP and RAFP.

Oceania: 

Australia: In Australia, Service Police refers to services policing three different military branches:

The 1st Military Police Battalion is the field component of the Military Police and the Domestic Policing Unit is the garrison policing component. In the Australian Army, the Royal Australian Corps of Military Police also performs the role of a secondary communications network in the front battle zone. Army MP's wear a red shoulder patch with MP in black.
In the Royal Australian Navy, the Naval Police Coxswain Branch performs dual roles of performing general police duties, investigation of criminal offences and a secondary role of ships' coxswain staff responsible for administration of ships' personnel.
In the Royal Australian Air Force, the Air Force Police perform the military police role. The Air Force Police organisation falls within Security Forces, therefore their role is largely providing force protection and enforcing military and civilian laws. Air Force Police members wear either a black brassard or patch with white SP meaning Service Police.
The Royal Australian Corps of Military Police train their own working dogs for a more Infantry/combat role.
All major crimes committed by or against personnel of the Australian Defence Force are investigated by the Australian Defence Force Investigative Service.

New Zealand: The Joint Military Police Unit (JMPU) is a tri-service Military Police unit from the Navy, Army, and Air Force.
JMPU comprises military police personnel from the Royal New Zealand Navy Naval Police, Royal New Zealand Military Police, and the Royal New Zealand Air Force Police. Personnel still maintain their own single service identity but operate under a single Provost Marshal and investigate offences against the Armed Forces Discipline Act 1971.
JMPU operates outside of the normal Navy, Army and Air Force command structure. The current Provost Marshal is a Group Captain who reports directly to the Vice Chief of the NZDF.

For all serious and complex investigations that are outside the scope of regular Military Police personnel a specialised unit known as the Special Investigations Branch (SIB) handles all high-profile investigations. SIB personnel attend courses with the New Zealand Police Criminal Investigation Branch. SIB have a similar role to the Australian Defence Force Investigative Service (ADFIS). SIB are also seconded to the NZ Police CIB.
JMPU also provide the close protection function for the NZDF. Only personnel from within the unit are able to attend the Tier 1 course and undergo a rigorous selection process. From time to time NZ Police officers from the Diplomatic Protection Squad and the Armed Offenders Squad have been known to also complete the course.
JMPU complete certain NZ Police courses such as Urgent Duty Driving, Disaster Victim Identification, Basic and Intermediate Crash Investigation with the NZ Police Serious Crash Unit, and some personnel have completed the Diplomatic Protection Squad training course.
JMPU are responsible for all detainee handling both in peacetime and in an operational environment such as custody and escort of POWs. Military Police are responsible for maintaining discipline at the Services Correction Establishment (SCE) which is located at Burnham Military Camp. SCE is the NZDF Military Prison and consists of guards who are all serving members of JMPU. The guards are responsible for rehabilitation of service personnel who have been sent to the facility as a result of serious offences committed against the Armed Forces Discipline Act 1971.
JMPU are identifiable by the blue and white "MP" patch they wear on their uniform and the blue beret as head dress, the wearing of the Blue beret differs from many commonwealth military police units as traditionally a red beret is worn.
JMPU wear their respective service dress for each service. During peacetime JMPU wear either a Multicam Camouflage uniform, or blue uniform with a SRBA vest.

Air force police: Air force police or sometimes known as "Air police" refers to certain units that are part of a country's air force that perform law enforcement duties such as force protection and air patrols, dealing primarily with the enforcement of aviation law at air force bases. It also indirectly plays a part in ensuring the air sovereignty of a country. It serves similarly to military and paramilitary police forces around the world and are commonly set up as a branch of a nation's military police or even a separate institution altogether. In some countries, the Air force police are also responsible for conducting Provost duties in the scope of a country's air force, such as implementing crime investigation and enforcing discipline/order towards members of the Air force.

By country: Royal Australian Air Force Air Force Police
 Canadian Forces Military Police The Air Force Military Police Group
 Air Gendarmerie
 Indian Air Force Police
 Indonesian Air Force Military Police Command (Puspomau).
 Air Police Group, Japan Air Self-Defense Force
 Air Force Police, Royal Air Force Regiment
 Royal New Zealand Air Force Police
 Polícia Aérea
 Military police of the Republic of Korea Air Force
 Sri Lanka Air Force
 Turkish Air Force
 Royal Air Force Police
 No. 3 (Royal Auxiliary Air Force) Police Squadron
 United States Air Force Security Forces
 Venezuela Air Force Police

See also: Military police vehicle
Police tactical unit
Separation of military and police roles

References: 

External links:  Media related to Military police at Wikimedia Commons