Graduate subjects (or courses) are commonly offered in graduate courses and can provide specialized knowledge of different topics that are important for the formation of Ph.D. and Master's students. At the same time, Systematic Literature Review (SLR) has been increasingly adopted in the computing area as a research method to synthesize the state of the art of a given research topic, identify research groups working on that topic, understand the existing limitations and research gaps, and also identify new research directions. However, it is still not well understood the real benefits and drawbacks of offering a subject that addresses SLR for graduate students. Moreover, it is not known the difficulties faced by professors (i.e., educators) to teach this subject. The main goal of this work is to present an experience report of teaching SLR, in particular, the benefits and drawbacks of this subject for computer science graduate students. In addition, this work also presents the essential topics of SLR that we recommend to be taught and a better way to teach them, aiming at supporting graduate courses to offer it. For this, we surveyed computer science graduate students who attended the SLR subject that was taught for almost ten years in our institutions. In particular, we collected the lessons learned, findings, and insights; following, we summarized the benefits and drawbacks for students, the difficulties for professors, and also those essential topics to be taught. As a main result, the SLR subject can be considered a valuable opportunity for graduate students that could use this subject to conduct the required deep literature review of their research topic and have a better comprehension of their research area. Besides and more importantly, this subject can improve important research skills of students, including the ability to recognize research problems, analyze and synthesize data, think critically, and write papers. Therefore, we believe that graduate courses should analyze the possibility of offering the SLR subject.