Background: The worldwide software ecosystem is a trust-rich part of the world. Throughout the software life cycle, software engineers, software end-users, and other stakeholders collaboratively place their trust in major hubs in the ecosystem, such as package managers, repository services, and software components. However, as our reliance on software grows, this trust is frequently violated by bad actors and crippling vulnerabilities in the software supply chain, endangering our livelihoods and the resilience of our society. Purpose: The purpose of this study is to define trust in the worldwide software ecosystem, that is, to determine what signifies a trustworthy system or actor. By improving our understanding of trust, we can create novel mechanisms for protecting the software ecosystem from vulnerabilities and attacks. Methods: We conduct a systematic literature review on the concept of trust in the worldwide software ecosystem. We acknowledge that trust is something between two actors in the software ecosystem, and we examine what role trust plays in the relationships between end-users and (1) software products, (2) package managers, (3) software producing organizations, and (4) software engineers. Results: Two major findings emerged from the systematic literature review. To begin, we provide a definition of trust in the software ecosystem, including a theoretical framework that decomposes and signifies a theoretical understanding of trust. Second, we provide a list of trust factors that can be used to assemble an overview of software trust. Conclusion: Trust is critical in the communication between actors in the worldwide software ecosystem, particularly regarding software selection and evaluation, and can affect the outcome either positively or negatively. According to the frequency