Abstract: In this paper, we study the problem of extracting variable-depth "logical document hierarchy" from long documents, namely organizing the recognized "physical document objects" into hierarchical structures. The discovery of logical document hierarchy is the vital step to support many downstream applications (e.g., passage-based retrieval and high-quality information extraction). However, long documents, containing hundreds or even thousands of pages and a variable-depth hierarchy, challenge the existing methods. To address these challenges, we develop a framework, namely Hierarchy Extraction from Long Document (HELD), where we "sequentially" insert each physical object at the proper position on the current tree. Determining whether each possible position is proper or not can be formulated as a binary classification problem. To further improve its effectiveness and efficiency, we study the design variants in HELD, including traversal orders of the insertion positions, heading extraction explicitly or implicitly, tolerance to insertion errors in predecessor steps, and so on. As for evaluations, we find that previous studies ignore the error that the depth of a node is correct while its path to the root is wrong. Since such mistakes may worsen the downstream applications seriously, a new measure is developed for a more careful evaluation. The empirical experiments based on thousands of long documents from Chinese financial market, English financial market and English scientific publication show that the HELD model with the "root-to-leaf" traversal order and explicit heading extraction is the best choice to achieve the tradeoff between effectiveness and efficiency with the accuracy of 0.972,6, 0.729,1 and 0.957,8 in the Chinese financial, English financial and arXiv datasets, respectively. Finally, we show that the logical document hierarchy can be employed to significantly improve the performance of the downstream passage retrieval task. In summary, we conduct a systematic study on this task in terms of methods, evaluations, and applications.