A Communist Party is a political party with a doctrine that is based on the principles of the The Communist Manifesto.
A political party described as a Communist party includes those that advocate the application of the socio-economic principles of scientific socialism (Marxism) as advocated by Karl Marx and Friedrich Engels in the 1848 tract The Communist Manifesto, through an intermediary period of socialism with the intended goal of arriving at a stateless/classless society i.e communism/anarchy.
A few examples of communist parties:
Communist Party of the Soviet Union
The Communist Party of the Soviet Union (Russian: Коммунистическая партия Советского Союза, Kommunisticheskaya partiya Sovetskogo Soyuza; short: КПСС, KPSS) was the only legal, ruling political party in the Soviet Union and one of the largest communist organizations in the world. It lost its dominance with the dismantling of the Soviet Union.
It emerged from the Bolshevik faction of the Russian Social Democratic Labour Party, under the leadership of Vladimir Lenin and Leon Trotsky. The party led the 1917 October Revolution that overthrew the Russian Provisional Government . Its organization was subdivided into communist parties of the constituent Soviet Republics as well as the mass youth organization, Komsomol. The party was also the driving force of the Third International (Comintern).
Communist Party of China
The Communist Party of China (CPC), also known as the Chinese Communist Party (CCP), is the founding and ruling political party of the People's Republic of China (PRC). Although nominally it exists alongside the United Front, in practice, the CPC is the only party of the PRC, maintaining a unitary government centralizing the state, military, and media. The legal power of the Communist Party is guaranteed by the PRC constitution.
The party was founded in July, 1921 in Shanghai. After a lengthy civil war, the party defeated its primary rival, the Kuomintang (KMT), and expanded into all of mainland China. by 1949. The Kuomintang retreated to the island of Taiwan, which it still retains to this day.
The party has fluctuated between periods of reform and political conservatism throughout its history. In the modern party, the topic of reform and liberalisation remains a contentious issue heavily debated among top officials.
Notable Leaders: Mao Zedong
Communist Party of Cuba
The Communist Party of Cuba (Spanish: Partido Comunista de Cuba, PCC) is the governing political party in Cuba. It is a communist party of the Marxist-Leninist model. The Cuban constitution ascribes the role of the Party to be the "leading force of society and of the state". As of April 2011, the First Secretary of the Communist Party of Cuba is Raúl Castro, the President of Cuba, younger brother of the previous First Secretary and President of Cuba, Fidel Castro, and the Second Secretary is José Ramón Machado Ventura.
Notable Leaders: Fidel Castro, Che Guevara.
Workers' Party of Korea
Communist movement in Korea intensified after World War II. The Communist North's clashes with the Democratic South resulted in the Korean War, which technically still continues to this day. The former Soviet Union once backed the country financially, and since its dissolution in the late 80's, North Korea falls into great debt and poverty. The Party's "Eternal President" is Kim Il Sung (yes, he's still the acting president, even when he's dead), followed by his son Kim Jong Il the General Secretary and later his grandson Kim Jong Un.
Notable Leaders: Kim Il Sung, Kim Jong-il, Kim Jong-Un
In Downfall Universe
The Communist Party is the main enemy of the Nazi Party in many Downfall parodies.