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Point cloud data have been widely explored due to its superior accuracy and robustness under various adverse situations. Meanwhile, deep neural networks (DNNs) have achieved very impressive success in various applications such as surveillance and autonomous driving. The convergence of point cloud and DNNs has led to many deep point cloud models, largely trained under the supervision of large-scale and densely-labelled point cloud data. Unsupervised point cloud representation learning, which aims to learn general and useful point cloud representations from unlabelled point cloud data, has recently attracted increasing attention due to the constraint in large-scale point cloud labelling. This paper provides a comprehensive review of unsupervised point cloud representation learning using DNNs. It first describes the motivation, general pipelines as well as terminologies of the recent studies. Relevant background including widely adopted point cloud datasets and DNN architectures is then briefly presented. This is followed by an extensive discussion of existing unsupervised point cloud representation learning methods according to their technical approaches. We also quantitatively benchmark and discuss the reviewed methods over multiple widely adopted point cloud datasets. Finally, we share our humble opinion about several challenges and problems that could be pursued in future research in unsupervised point cloud representation learning. A project associated with this survey has been built at https://github.com/xiaoaoran/3d_url_survey.