Article snapshot taken from Wikipedia with creative commons attribution-sharealike license.
Give it a read and then ask your questions in the chat.
We can research this topic together.
The most recent (since 31 May 1998) king, Tito, was deposed by a vote of no confidence in the Leadership Council, and was replaced (on 30 May 2004) by Valentín. The former, who is no longer in office, has disputed the legality of the deposition, and still claims the title. The new king has not yet been recognised by the government of Panama.
Succession is determined by the vote of the general adult population. An election for a new monarch may take place upon any occasion in which an eligible member of the royal family wishes to be considered. Until recently, the traditional law of succession followed a pattern similar to the rota system.
Asia
Indonesia
Others
The Bohmong Raja is recognised by the government of Bangladesh as the leader of the Marma population, and the traditional king of the Bohmong Circle (Bohmong Htaung), one of three tribal circles in the Chittagong Hill Tracts.
The Chakma Raja is recognised by the government of Bangladesh as the leader of the Chakma population, and the traditional king of the Chakma Circle, one of three tribal circles in the Chittagong Hill Tracts.
The Mong Raja is recognised by the government of Bangladesh as the leader of the Arakanese population, and the traditional king of the Mong Circle (Phalang Htaung), one of three tribal circles in the Chittagong Hill Tracts.
After the neighbouring kingdom of Ambeno was annexed in 1912, it changed its name to Oecusse-Ambeno.
Antonio was recognised as liurai in 2001, but has not yet been officially installed. He presently acts as regent.
The kings of the five traditional states known collectively as the Dangs are the only royals in India whose titles are recognised by the government. Each raja receives an annual pension from the state, owing to an agreement made with the British colonial government in 1842.
The current Raja of Gadhvi has been missing since 1992. His son and heir, Karan Singh, is presently acting as prince regent.
These five traditional chiefdoms are part of the confederacy of Negeri Sembilan, a federated state of Malaysia. The ruling chiefs of Jelebu, Johol, Rembau, and Sungai Ujong form the Undang Laut, who will decide the next Yang di-Pertuan Besar of Negeri Sembilan. Tampin is a separate hereditary principality.
Formally enthroned on 20 November 1981.
The undang (ruling chief) is elected for life by the nobles and vassals of the state from amongst the three highest noble families: the Waris Ulu Jelebu, Waris Sarin, and Waris Kemin.
The undang (ruling chief) is elected for life by the nobles and vassals of the state from amongst the male descendants of the first ruler, following the matrilineal line.
The undang (ruling chief) is elected for life by the nobles and vassals of the state from amongst the direct descendants of two noble families: the Waris Jakun and Waris Jawa. The position is, by informal agreement, alternated between the heads of the two houses.
The undang (ruling chief) is elected for life by the nobles and vassals of the state from amongst the direct descendants of two noble families: the Waris Hulu and Waris Hilir.
Formally enthroned on 12 August 2006.
The Yang di-Pertuan Muda (prince) succeeds according to the laws of male primogeniture, but must also receive confirmation from the reigning Yang di-Pertuan Besar of Negeri Sembilan.
Europe
Oceania
The government of the Marshall Islands recognises a total of twelve chiefly domains, called mojen, each headed by one or several paramount chiefs. Each domain is represented in the Council of Iroij, a legislative body of traditional chiefs guaranteed by the Constitution.
This chief is normally referred to as the Isipahu.
The ruling line belongs specifically to the Inenkatau (or Upwutenmai) sept of the Dipwinpahnmei clan.
This chief is normally referred to as the Sangiro.
The ruling line belongs specifically to the Sounpasedo sept of the Lasialap clan.
Hilarion was recognised as grand chef in 1974, but, due to a violent succession dispute with his relative Jean-Marie Vendégou, was not formally enthroned until later, on 7 July 1979. He is also the incumbent mayor of the island commune, until 2014.
The Naisseline family is a branch of the Netché, a tribe of Kanaks.
The throne of the grand chef on Maré Island is traditionally held by the chief of Guahma district, which is an hereditary position.
The throne of the grand chef on Lifou Island, which also rules over Ouvéa, is traditionally held by the chief of Lössi district, an hereditary position.
Commonly referred to as the "Māori King Movement". Its elected ariki nui is often called the "Māori King" due to his nationalistic influence over all Māori tribes as a symbol of unity. This title is not recognised by the government of New Zealand.
Te Wherowhero is the lineage of the first king. It belongs to the Waikato iwi, which is part of the Tainui confederation.
The monarch is appointed for life by the chiefs of the various tribes involved in the Kīngitanga movement. Traditionally, selection is limited to direct descendants of the first king: Pōtatau I, who was from the Waikato tribe. However, on principal, inheritance is open to any lineage should the electing chiefs be in agreement.
Palau is divided into 16 traditional polities. The 16-seat Council of Chiefs, which is made up of the traditional chiefs from each constituent state, is an advisory body to the President. The chiefs of Koror and Melekeok, the highest chiefs from Eoueldaob and Babeldaob respectively, are recognised as the two paramount chiefs of the nation.
^ This is not the name of the ruling house or clan. It is instead the ritual name used by the successive chiefs from this lineage.
^ Chiefs are selected by the seniormost women of the ruling clan.
Each island or atoll of Tuvalu has a traditional high chief, the ulu-aliki, who is recognised by and plays an active ceremonial role in the national government. Thrones are primarily elective, but candidates are limited to members of a certain number of chiefly clans.
Funafuti's traditional chieftaincy is limited to senior members of two chiefly clans. By custom, succession rotates between the two lineages.
The high chief, or Pulefenua, is elected by a council of chiefs (the Fale Kaupule) from amongst senior members of Nanumea's seven chiefly clans, all of which claim descent from the island's first settlers.
Government of Tuvalu; Ministry of Finance, Economic Planning and Industries; Economic Research and Policy Division (2005), "Malefatuga Declarartion", Te Kakeega II: National Strategies for Sustainable Development: 2005–2015 (PDF), Funafuti: United Nations, p. 27, retrieved 2010-06-14 {{citation}}: |author= has generic name (help); Cite has empty unknown parameter: |chapterurl= (help); Unknown parameter |month= ignored (help)CS1 maint: multiple names: authors list (link).
Panama
Bangladesh
East Timor
India 
Malaysia 
Cook Islands
Marshall Islands 
FSM
New Caledonia
New Zealand
Palau 
Tuvalu