Code comments are important artifacts in software systems and play a paramount role in many software engineering (SE) tasks related to maintenance and program comprehension. However, while it is widely accepted that high quality matters in code comments just as it matters in source code, assessing comment quality in practice is still an open problem. First and foremost, there is no unique definition of quality when it comes to evaluating code comments. The few existing studies on this topic rather focus on specific attributes of quality that can be easily quantified and measured. Existing techniques and corresponding tools may also focus on comments bound to a specific programming language, and may only deal with comments with specific scopes and clear goals (e.g., Javadoc comments at the method level, or in-body comments describing TODOs to be addressed). In this paper, we present a Systematic Literature Review (SLR) of the last decade of research in SE to answer the following research questions: (i) What types of comments do researchers focus on when assessing comment quality? (ii) What quality attributes (QAs) do they consider? (iii) Which tools and techniques do they use to assess comment quality?, and (iv) How do they evaluate their studies on comment quality assessment in general? Our evaluation, based on the analysis of 2353 papers and the actual review of 47 relevant ones, shows that (i) most studies and techniques focus on comments in Java code, thus may not be generalizable to other languages, and (ii) the analyzed studies focus on four main QAs of a total of 21 QAs identified in the literature, with a clear predominance of checking consistency between comments and the code. We observe that researchers rely on manual assessment and specific heuristics rather than the automated assessment of the comment quality attributes, with evaluations often involving surveys of students and the authors of the original studies but rarely professional developers.