Cloud computing refers to the delivery of computer processing infrastructure, operating systems, software and data storage over Internet-based public or private computer networks. The aim is to relieve users of some of the burdens associated with maintaining computers and data storage, while enabling the associated costs to be reduced. Although cloud computing is still developing in popularity and coverage, its use raises a number of crime and security concerns, particularly for small business users. This paper charts the nature of these concerns for small business and reviews the detection, prevention and mitigation measures that may be implemented by small business users and cloud service providers to minimise or negate the risks identified.