Neural network pruning typically removes connections or neurons from a pretrained converged model; while a new pruning paradigm, pruning at initialization (PaI), attempts to prune a randomly initialized network. This paper offers the first survey concentrated on this emerging pruning fashion. We first introduce a generic formulation of neural network pruning, followed by the major classic pruning topics. Then, as the main body of this paper, a thorough and structured literature review of PaI methods is presented, consisting of two major tracks (sparse training and sparse selection). Finally, we summarize the surge of PaI compared to PaT and discuss the open problems. Apart from the dedicated literature review, this paper also offers a code base for easy sanity-checking and benchmarking of different PaI methods.