Infant cry is evolutionarily, psychologically, and clinically significant. Over the last half century, several researchers and clinicians have investigated acoustical properties of infant cry for medical purposes. However, this literature suffers a lack of standardization in conducting and reporting cry-based studies. In this work, methodologies and procedures employed to analyze infant cry are reviewed and best practices for reporting studies are provided. First, available literatures on vocal and audio acoustic analysis are examined to identify critical aspects of participant information, data collection, methods, and data analysis. Then, 180 peer-reviewed research articles have been assessed to certify the presence of critical information. Results show a general lack of critical description. Researchers in the field of infant cry need to develop a consensual standard set of criteria to report experimental studies to ensure the validity of their methods and results.