Context: Jupyter Notebook has emerged as a versatile tool that transforms how researchers, developers, and data scientists conduct and communicate their work. As the adoption of Jupyter notebooks continues to rise, so does the interest from the software engineering research community in improving the software engineering practices for Jupyter notebooks. Objective: The purpose of this study is to analyze trends, gaps, and methodologies used in software engineering research on Jupyter notebooks. Method: We selected 146 relevant publications from the DBLP Computer Science Bibliography up to the end of 2024, following established systematic literature review guidelines. We explored publication trends, categorized them based on software engineering topics, and reported findings based on those topics. Results: The most popular venues for publishing software engineering research on Jupyter notebooks are related to human-computer interaction instead of traditional software engineering venues. Researchers have addressed a wide range of software engineering topics on notebooks, such as code reuse, readability, and execution environment. Although reusability is one of the research topics for Jupyter notebooks, only 64 of the 146 studies can be reused based on their provided URLs. Additionally, most replication packages are not hosted on permanent repositories for long-term availability and adherence to open science principles. Conclusion: Solutions specific to notebooks for software engineering issues, including testing, refactoring, and documentation, are underexplored. Future research opportunities exist in automatic testing frameworks, refactoring clones between notebooks, and generating group documentation for coherent code cells.