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Cross-lingual summarization is the task of generating a summary in one language (e.g., English) for the given document(s) in a different language (e.g., Chinese). Under the globalization background, this task has attracted increasing attention of the computational linguistics community. Nevertheless, there still remains a lack of comprehensive review for this task. Therefore, we present the first systematic critical review on the datasets, approaches, and challenges in this field. Specifically, we carefully organize existing datasets and approaches according to different construction methods and solution paradigms, respectively. For each type of datasets or approaches, we thoroughly introduce and summarize previous efforts and further compare them with each other to provide deeper analyses. In the end, we also discuss promising directions and offer our thoughts to facilitate future research. This survey is for both beginners and experts in cross-lingual summarization, and we hope it will serve as a starting point as well as a source of new ideas for researchers and engineers interested in this area.