Different groups have radically different understandings of what the abolition of governments would entail: "Libertarian socialists" are convinced it means a collectivist economy; "anarcho-capitalists" are convinced it means capitalism; "individualist anarchists" don't know or don't care as much about such issues, but insist above all on individual freedom from state.
Adherents of this view sometimes call themselves 'libertarian socialists' or 'left anarchists', to distinguish themselves from anarcho-capitalists. However, the mere word 'anarchist' popularly denote this brand of anarchists.
Libertarian socialism traces its tradition back to the eighteenth (can anyone give any reference???) and nineteenth centuries (see Proudhon, Kropotkin, Bakunin, etc.).
Few left-anarchists are actually violent, but throughout the late 19th and early 20th century, the violent kind has made "anarchism" famous as an ideology justifying murder and bombing. Most left-anarchists are not immediately violent, although many advocate a future revolution. The position of left-anarchists regarding violence, what legitimizes it or not, and how can justice exist with or without violence is not clear, though.
Adherents of this theory of anarchism call themselves 'anarcho-capitalists'.
Anarcho-capitalism has existed in its modern form at least since Gustave de Molinari in the 1840s, but has mostly been flourishing since it organized in the 1950s in the USA. Anarcho-capitalists consider themselves as radical members of the classical liberal tradition ('libertarianism' as it is now called in the USA), and trace their explicit roots back to Locke and the seventeenth century english Whigs. All classical liberals believe in 'as little government as possible'; anarchists among them believe governments can and must be done without completely, whereas minarchists believe or accept that some government be necessary for e.g. enforcing law and order.
Anarcho-capitalists, like classical liberals in general, tend to loathe violent action and revolutions as a "normal" way to promote or impose their views, even in presence of governments they hate. However, they do support, e.g. the american revolution, that precisely consisted in individuals sharing common views fighting together, against people trying to impose their views on them.
Like libertarian socialists, they loathe government-supported capitalism, and reject several essential principles of capitalism in general. Like anarcho-capitalists, they put an emphasis on individual rights and liberty, and on market-based approaches rather than collectivism. They are thus acknowledged both by libertarian socialists and anarcho-capitalists, although each side accepts or criticizes differently the works of these thinkers. See individualist anarchism for a discussion of this issue.
On the debate of capitalism vs socialism, the reply of modern individualist anarchism is to let each individual choose the system he is willing to adhere to, and, with experience, each will choose what suits him best; to them, it doesn't matter which system will majoritarily prevail, as long as individual freedom is respected.
This usage has strong negative connotations, and has historically been used as a slur by political groups against their opponents, most notably by monarchists against republicans in past centuries. However, anomy has also been embraced by countercultural elements such as punk rock.
Libertarian socialists consider that an employer-employee relationship is based on coercion by the employer, which constitutes a de facto government, and should be prevented, even if oppressed employees are passively consenting out of weakness and ignorance. Anarcho-capitalists consider that an employer-employee relationship is an elaborate and mutually profitable form of voluntary association, and that any external power capable of preventing it is a form of oppressive de facto government.
Libertarian socialists and anarcho-capitalists view each other with hostility. Proponents of each of these two theories tend to claim that theirs is the only true anarchism, while the other position is not anarchism at all, because it opposes a wrong notion of power ('archos'). On the other hand, libertarian socialists consider themselves as part of the collectivist movement, while anarcho-capitalists consider themselves as classical liberals - this shows that the opposition between collectivism and individualism in matters of political economy is indeed more essential than the question of the existence of government.
Many libertarian socialists argue that anarcho-capitalism should not be called anarchism at all, due to the much older use of the word to refer to libertarian socialism. Anarcho-capitalists argue they have just as much right to the word as libertarian socialists have, and that their anti-statist tradition is actually older and more coherent. Individualist anarchists don't care much for such macho "length contests" about the age of traditions.
Here is a small selection of most famous anarchists. For more, see in various categories.
Web sites with a clear libertarian socialist bent:
Web sites with a clear anarcho-capitalist bent:
See also: nihilism, syndicalism, libertarianism
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