There are many different views on this. Among left-anarchists, there are some who imagine returning to a much simpler, even pre-industrial, mode of social organisation. Others seem to intend to maintain modern technology and civilisation (perhaps in a more environmentally sound manner) but end private ownership of the means of production.
To be replaced with what? Various suggestions have been made. Existing firms might simply be turned over to worker ownership, and then be subject to the democratic control of the workers. This is the anarcho-syndicalist picture: Keeping an economy based upon a multitude of firms, but with firms owned and managed by the workers at each firm. Presumably firms would then strike deals with one another to secure needed materials; or perhaps firms would continue to pay money wages and sell products to consumers. It is unclear how the syndicalist intends to arrange for the egalitarian care of the needy, or the provision of necessary but unprofitable products. Perhaps it is supposed that syndicates would contribute out of social responsibility; others have suggested that firms would elect representatives for a larger meta-firm organisation which would carry out the necessary tasks.
It should be noted that Tom Wetzel disputes my characterisation of anarcho-syndicalism; he argues that very few anarcho-syndicalists ever imagined that workers would simply take over their firms, while maintaining the basic features of the market economy. Rather, the goal has usually been the establishment of an overarching democratic structure, rather than a multitude of uncoordinated firm-centred democracies. Or at Wetzel states, "Anarcho-syndicalism advocates the development of a mass workers' movement based on direct democracy as the vehicle for reorganisation of the society on the basis of direct workers' collective power over social production, thus eliminating the domination and exploitation of the producing class by an exploiting class. Workers cannot have collective power over the system of social production as isolated groups competing in a market economy; rather, workers self-management requires structures of democratic control over social production and public affairs generally. Workers' self-management thus refers, not just to self-management of the individual workplace, but of the whole system of social production. This requires grassroots bodies, such as workers' congresses or conventions, through which coordinated policies for the society can be developed in a democratic manner. This is proposed as a substitute or replacement for the historical nation-state." On this interpretation of anarcho-syndicalism, the revolutionary trade unions are a means for achieving an anarchist society, rather than a proposed basis for social organisation under anarchy.
Many would observe that there is nothing anarchistic about this proposal; indeed, names aside, it fits easily into the orthodox state-socialist tradition. Bakunin would have probably ridiculed such ideas as authoritarian Marxist socialism in disguise, and predicted that the leading anarchist revolutionaries would swiftly become the new despots. But Wetzel is perhaps right that many or even most historical anarcho-syndicalists were championing the system outlined in his preceding quotation. He goes on to add that "[I]f you look at the concept of 'state' in the very abstract way it often is in the social sciences, as in Weber's definition, then what the anarcho-syndicalists were proposing is not elimination of the state or government, but its radical democratisation. That was not how anarchists themselves spoke about it, but it can be plausibly argued that this is a logical consequence of a certain major stream of left-anarchist thought."
Ronald Fraser's discussion of the ideology of the Spanish Anarchists (historically the largest European anarchist movement) strongly undermines Wetzel's claim, however. There were two well-developed lines of thought, both of which favoured the abolition of the State in the broad Weberian sense of the word, and which did indeed believe that the workers should literally have control over their workplaces. After distinguishing the rural and the urban tendencies among the Spanish ideologists, Fraser explains:
Common to both tendencies was the idea that the working class 'simply' took over factories and workplaces and ran them collectively but otherwise as before . . . Underlying this vision of simple continuity was the anarcho-syndicalist concept of the revolution not as a rupture with, the destruction and replacement of, the bourgeois order but as the latter's displacement. The taking over of factories and workplaces, however violently carried out, was not the beginning of the revolution to create a new order but its final goal. This view, in turn was conditioned by a particular view of the state. Any state (bourgeois or working class) was considered an oppressive power tout court — not as the organisation of a particular class's coercive power. The 'state' in consequence, rather than the existence of the capitalist mode of production which gave rise to its particular form, often appeared as the major enemy. The state did not have to be taken, crushed, and a new — revolutionary — power established. No. If it could be swept away, abolished, everything else, including oppression, disappeared. The capitalist order was simply displaced by the new-won workers' freedom to administer the workplaces they had taken over. Self-organised in autonomous communes or in all-powerful syndicates, the workers, as the primary factor in production, dispensed with the bourgeoisie. The consequences of this were seen in the 1936 Barcelona revolution; capitalist production and market relations continued to exist within collectivised industry.
Overall, the syndicalist is probably the best elaborated of the left-anarchist systems. But others in the broader tradition imagine individuals forming communes and cooperatives which would be less specialised and more self-sufficient than the typical one-product-line anarcho-syndicalist firm. These notions are often closely linked to the idea of creating a more environmentally sound society, in which small and decentralised collectives redirect their energies towards a Greener way of life.
Many left-anarchists and anarchist sympathisers have also been attracted to Guild Socialism in one form or another. Economist Roger A. McCain thoughtfully explores Guild Socialism as an alternative to both capitalism and the state in "Guild Socialism Reconsidered," one of his working papers.
Kropotkin's lucid essay "Law and Authority" gives a thoughtful presentation of the left-anarchist's view of law. Primitive human societies, explains Kropotkin, live by what legal thinkers call "customary law": An unwritten but broadly understood body of rules and appropriate behaviour backed up primarily by social pressure. Kropotkin considers this sort of behavioural regulation to be unobjectionable, and probably consistent with his envisaged anarchist society. But when centralised governments codified customary law, they mingled the sensible dictates of tribal conscience with governmental sanctions for exploitation and injustice. As Kropotkin writes, "[L]egislators confounded in one code the two currents of custom . . . the maxims which represent principles of morality and social union wrought out as a result of life in common, and the mandates which are meant to ensure external existence to inequality. Customs, absolutely essential to the very being of society, are, in the code, cleverly intermingled with usages imposed by the ruling caste, and both claim equal respect from the crowd. 'Do not kill,' says the code, and hastens to add, 'And pay tithes to the priest.' 'Do not steal,' says the code, and immediately after, 'He who refuses to pay taxes, shall have his hand struck off.'"
So perhaps Kropotkin's ideal society would live under the guidance of a reformed customary law stripped of the class legislation with which it is now so closely associated. But Kropotkin continues to give what appear to be arguments against even customary law prohibiting e.g. murder. Almost all violent crime is actually caused by poverty and inequality created by existing law. A small residual of violent crime might persist, but efforts to handle it by legal channels are futile. Why? Because punishment has no effect on crime, especially such crimes of passion as would survive the abolition of private property. Moreover, criminals should not be judged wicked, but rather treated as we now treat the sick and disadvantaged.
Most left-anarchists probably hold to a mix of Kropotkin's fairly distinct positions on law and crime. Existing law should be replaced by sensible and communitarian customs; and the critic of anarchism underestimates the extent to which existing crime is in fact a product of the legal system's perpetuation of inequality and poverty. And since punishment is not an effective deterrent, and criminals are not ultimately responsible for their misdeeds, a strictly enforced legal code may be undesirable anyway.
Some other crucial features of the left-anarchist society are quite unclear. Whether dissidents who despised all forms of communal living would be permitted to set up their own inegalitarian separatist societies is rarely touched upon. Occasionally left-anarchists have insisted that small farmers and the like would not be forcibly collectivised, but the limits of the right to refuse to adopt an egalitarian way of life are rarely specified.