Obtaining effective molecular representations is at the core of a series of important chemical tasks ranging from property prediction to drug design. So far, deep learning has achieved remarkable success in learning representations for molecules through automated feature learning in a data-driven fashion. However, training deep neural networks from scratch often requires sufficient labeled molecules which are expensive to acquire in real-world scenarios. To alleviate this issue, inspired by the success of the pretrain-then-finetune paradigm in natural language processing, tremendous efforts have been devoted to Molecular Pre-trained Models (MPMs), where neural networks are pre-trained using large-scale unlabeled molecular databases and then fine-tuned for diverse downstream tasks. Despite the prosperity, this field is fast-growing and a systematic roadmap is urgently needed for both methodology advancements and practical applications in both machine learning and scientific communities. To this end, this paper provides a systematic survey of pre-trained models for molecular representations. Firstly, to motivate MPMs studies, we highlight the limitations of training deep neural networks for molecular representations. Next, we systematically review recent advances on this topic from several key perspectives including molecular descriptors, encoder architectures, pre-training strategies, and applications. Finally, we identify several challenges and discuss promising future research directions.