Infant cry is evolutionarily, psychologically, and clinically significant. During the last 60 years, several researchers and clinicians assessed the possibility of investigating the acoustical properties of cry for medical purposes. However, there is a lack of standardization in conducting and reporting cry-based studies. In this work, methodologies and procedures employed in infant cry analysis are reviewed, and best practices for reporting studies are provided. First, available literature on vocal and audio acoustic analysis have been 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 identified critical information. Results show a general lack of critical description. Researchers in the field of infant cry need to agree on a standard set of criteria to report experimental studies, to better demonstrate the validity of the methods and obtained results.