Online Social Networks (OSNs) are an integral part of the modern lifestyle, and the use of OSN is highly prevalent today. OSNs have enabled the generation of unprecedented quantities of data on users, their interests, relationships, actions, opinions, locations visited, items purchased, and their experiences in various aspects of life. Data and information related to reputation and influence exist on OSNs and are hidden. The objective of this study is to provide a better and deeper understanding and a detailed review of the current state of research pertaining to the measurement of reputation and influence in OSNs, specifically Twitter. We conducted a Systematic Literature Review to collect, analyze, and synthesize data on the accuracy and value of previous literature that has focused on this field, has addressed a variety of topics, and has been published in digital databases between 2010 and September 2019. We followed a predefined review procedure that integrated both automatic and manual search strategies to cover all relevant research papers published in this period.