We present a novel network pruning algorithm called Dynamic Sparse Training that can jointly find the optimal network parameters and sparse network structure in a unified optimization process with trainable pruning thresholds. These thresholds can have fine-grained layer-wise adjustments dynamically via backpropagation. We demonstrate that our dynamic sparse training algorithm can easily train very sparse neural network models with little performance loss using the same training epochs as dense models. Dynamic Sparse Training achieves prior art performance compared with other sparse training algorithms on various network architectures. Additionally, we have several surprising observations that provide strong evidence to the effectiveness and efficiency of our algorithm. These observations reveal the underlying problems of traditional three-stage pruning algorithms and present the potential guidance provided by our algorithm to the design of more compact network architectures.