In 5G and beyond, the figure of cross-operator/domain connections and relationships grows exponentially among stakeholders, resources, and services, with reputation-based trust models being one of the capital technologies leveraged for trustworthy decision-making. This work studies novel 5G assets on which trust can be used to overcome unsuitable decision-making and address current requirements. First, it introduces a background and general architecture of reputation-based trust models. Then, it analyzes pivotal 5G assets on which trust can enhance their performance. In addition, this article performs a comprehensive review of the current reputation models applied to 5G assets and compares their properties, features, techniques, and results. Finally, it provides current trends and future challenges to conducting forthcoming research in the area.