One of the many critiques of anarchist theory is that it lacks a solid constitutional framework for individuals to use as a reference to live and organize within society at large. This is not to suggest that theoreticians of anarchist ideas were/are naive to the problems and challenges society had/has to contend with or anarchist sympathizers (in general) promote chaos and/or lawlessness. On the contrary, by investigating the various anarchist "schools of thought" such as anarcho-syndicalism, anarcho-communism, anarcho-capitalism etc, there are a plethora of ideas and theories on how to deal with crime. Here lies the beauty of anarchism.
One of the fundamental principles of anarchism suggests that central authoritarian rule is immoral and should be replaced with non-hierarchically based organizations and voluntary associations. Within this framework, individual members of society will have to bare the responsibility of solving the major issue of crime in a dialogical manner. Let's not forget, unless a policy which allows for the extermination of sympathizers of the pre-revolutionary society were to unfold, social organization would include criminal experts, lawyers, statisticians, criminal psychologists, judges, police etc and clearly their expertise would be of great importance in solving the issues of crime.
Obviously, crime is a very difficult problem. A problem that most if not all cultures and societies have yet to solve conclusively and so there should be little reason to believe anarchism could provide a panacea. However, dialogical analysis could suggest solutions and alternatives to state authorized capital punishment, high rates of incarceration, unauthorized police force, crime due to mental illness, domestic abuse, capital crimes, drug related crimes, serial crimes etc.
Some believe that crime prevention through education and social development would be an obvious byproduct of an anarchist society. Although not ideal, police may have a very limited mandate in order to protect individual rights. Violent individuals may be treated using the latest psychological and neurological techniques as opposed to simple methods of incarceration. Petty crimes and personal safety may be dealt with on a community level. Justice and the law of the land would protect civil liberties.
The problems and solutions are truly limitless. It has become very hard for the laymen to understand the scope of the issues and their respective solutions but this may be the result of the transfer of reason and responsibility to the system of central authority. Clearly, governmental individual members of society engineer policy, however, within a completely different system such as anarchy, those same expert resources would be needed to tackle the issues at hand.
This answer is intentionally vague in the spirit of critical consciousness (as opposed to conclusive, irrationally biased, authoritarian opinion).