Trust has stood out more than ever in the light of recent innovations. Some examples are advances in artificial intelligence that make machines more and more humanlike, and the introduction of decentralized technologies (e.g. blockchains), which creates new forms of (decentralized) trust. These new developments have the potential to improve the provision of products and services, as well as to contribute to individual and collective well-being. However, their adoption depends largely on trust. In order to build trustworthy systems, along with defining laws, regulations and proper governance models for new forms of trust, it is necessary to properly conceptualize trust, so that it can be understood both by humans and machines. This paper is the culmination of a long-term research program of providing a solid ontological foundation on trust, by creating reference conceptual models to support information modeling, automated reasoning, information integration and semantic interoperability tasks. To address this, a Reference Ontology of Trust (ONTrust) was developed, grounded on the Unified Foundational Ontology and specified in OntoUML, which has been applied in several initiatives, to demonstrate, for example, how it can be used for conceptual modeling and enterprise architecture design, for language evaluation and (re)design, for trust management, for requirements engineering, and for trustworthy artificial intelligence (AI) in the context of affective Human-AI teaming. ONTrust formally characterizes the concept of trust and its different types, describes the different factors that can influence trust, as well as explains how risk emerges from trust relations. To illustrate the working of ONTrust, the ontology is applied to model two case studies extracted from the literature.