The article elucidates certain theoretical and legal issues that arise in the implementation of the constitutional right of citizens to petition. Throughout the research, the author presents definitions for the following terms: «right to petition», «petition», «constitutional right to personal appeal», «constitutional right to individual appeal», and «constitutional right to collective appeal». The author determines their distinctive characteristics. Additionally, the paper examines the specific terms established in the specialized law, namely «organizations entrusted with the performance of public significance functions» and «citizens entitled to receive personal reception as a priority». The author provides an interpretation of these terms. Based on an analysis of empirical material that includes examples of personal receptions conducted in public authorities, the author suggests a classification of types of personal reception. The research findings indicate a necessity for amendments to the Federal Law No. 59‑FZ of dated 2 May 2006, «On the Procedure for Considering Appeals from Citizens of the Russian Federation». Furthermore, the paper provides for suggestions for enhancing the specialized law governing the process of addressing petitions.