Here is a BBC overview for those who have no idea what I'm talking about, and want some kind of reference point.
When the Zapatistas began their rebellion twenty years ago, they were unleashing new currents of libertarian socialism and drawing from long traditions of indigenous resistance and communitarian values. Pre-Columbian indigenous America was as socially diverse as any other continent, and even in the colonial era, it's difficult to paint all indigenous peoples with a broad brush. Still, the indigenous Mayan communities in southern Mexico should be noted for their strong communal nature. The development of the hacienda system during the colonial era, then, introduced a strictly hierarchical system of private landownership that clashed with these indigenous farming communities.
The haciendas, large estates owned by members of a small economic elite and worked by dispossessed campesinos (peasants), outlived the colonial system that had birthed them. There's a lot of Mexican history to cover here, but I'm trying to get to the Zapatistas quickly. Before the Mexican Revolution, the country was under the rule of Porfirio Díaz, indirectly and directly, from 1876 until 1911, a period known as the Porfiriato. To quote a post on the Mexican Revolution I made six months ago, "The Porfiriato was characterized by a corrupt ruling elite, repression of civil liberties, heavy foreign ownership of Mexican land and industry, rapid economic growth, a modernization of the country, and the growth of the cities. The loss of communal lands (and corresponding growth of the haciendas) created a climate of alienation amongst the indigenous and rural peoples that would lead to the explosion of the Mexican Revolution in 1910."
When the Mexican Revolution did come, it was less one revolution and more many revolutions. Liberal frustration with the Porfirian dictatorship, led by Francisco Madero, unwittingly opened the door for the radical movements to rise to greater prominence in Mexico. Ricardo Flores Magón, the anarchist labor organizer who had been a major figure in resistance to the Porfiriato and was exiled before the Revolution, led a short-lived anarchist communist revolution in Baja California in 1911 and was a figure of influence on the large anarcho-syndicalist labor movement centered in Mexico City. Among the other radicals his writings helped inspire was perhaps the most famous figure out of the Mexican Revolution, Emiliano Zapata. Leader of a great army of dispossessed peasants and indigenous peoples in the south of Mexico, Zapata fought for major land reform, ultimately assassinated in 1919 by the state that had emerged from the Revolution. A version of his plan for land reform had been included in the Constitution of 1917, however, and his imagine would be used for decades to come by the Mexican state. I'm greatly oversimplifying the Revolution here, for brevity, as there were a lot of ideologies and factions at play.
Eventually, the state produced by the Revolution was consolidated and institutionalized under the National Revolutionary Party (PNR), which would become the Party of the Mexican Revolution (PRM) and, eventually, the Institutional Revolutionary Party (PRI). This party would become the longest ruling political party in the world, staying in constant power from 1929 to 2000. During this period, the ideological orientation of the party fluctuated. Under leftist President Lázaro Cárdenas (1934-40), the oil industry was nationalized, labor rights were expanded, and land reform accelerated. However, later presidents were more capitalist. Political repression also picked up, with the Tlatelolco Massacre in 1968 and the mass voter fraud against presidential candidate Cuauhtémoc Cárdenas (son of the late president, who broke from the PRI) in 1988. By the 1990s, the PRI was ready to fully embrace neoliberalism and the Washington Consensus.
Land reform had effectively slowed to a crawl by this time, but the final straw that sparked the Zapatista uprising was the signing of the North American Free Trade Agreement (NAFTA). It required the stripping of Article 27 of the 1917 Constitution, removing the provision for land redistribution, allowing the foreign ownership of Mexican land, and removing protections for communal indigenous land. Zapata's key ideological contributions to the Mexican state, after a long period of infidelity, were effectively destroyed. Thousands of poor and dispossessed indigenous farmers lost their only hope when land reform was ended. A group of mostly indigenous leftists, radicalized by increasing repression and neoliberal capitalism from the Mexican state, had been organizing for a decade, but really gained traction with the communities following these new developments.
So, on 1 January 1994, the day the NAFTA came into effect, the Zapatista Army of National Liberation (Ejército Zapatista de Liberación Nacional, "EZLN") declared war on the Mexican state and 3,000 guerrilleros seized control of much of the state of Chiapas. Though they had no centralized leaders, their spokesman, Subcomandante Marcos, cut a dramatic figure that immediately seized the public imagination. The EZLN immediately released its revolutionary program, the [First] Declaration of the Lacandona Jungle (early EZLN documents available here). They made clear the libertarian socialist nature of their revolution, with "revolutionary laws" surrounding labor, agrarian, and women's rights. For two weeks, they fought the Mexican state until a ceasefire was called. Pushed out of the major cities and much of the state, they retained (and still retain) control over a significant portion of indigenous territory.
Marcos began giving interviews and the EZLN made use of the internet to raise global awareness of their struggle and build pressure on the Mexican state. An uneasy standoff has persisted since, allowing the Zapatistas to focus on the governance of their territories and national and global advocacy for their ideology, rather than on constant violence. Though their governance style has been heavily influenced by anarchism and libertarian socialism/communism, the EZLN has rejected all political labeling other than "Zapatismo," and has not actually demanded the disillusion of the Mexican state so much as its fundamental transformation and decentralization. The Zapatistas claimed to be engaging in the Fourth World War, against the forces of neoliberalism, which had emerged victorious from the Third World War (what we would call the Cold War). It's hard to keep within the 20-year rule here, because there have been so many developments in the indigenous liberation movement since 1994, from the growth of the participatory democracy of the Good Government Councils to the launching of the nationwide "Other Campaign" to the anarchist "Oaxaca Commune" in the neighboring state.
The Zapatista rebellion was not an immediate success in that they neither precipitated the overthrow of the Mexican state, nor retained control of the state of Chiapas at large. However, the EZLN did hold on to territory spanning many indigenous communities, in which the line between community member and Zapatista has been blurred, and has been very successful in propagating a new ideology of communitarian socialism and indigenous liberation in an era of neoliberalism. Though 1994 is now fair game for questions here, the Zapatistas are certainly not history in the sense of belonging strictly to the past, as they are as active now as ever. They continue their struggle and have become radical icons for solidarity and resistance in the global struggle against modern neoliberal capitalism in the developing world over the last twenty years.