Trustworthiness is one of the main aspects that contribute to the adoption/rejection of a software product. This is actually true for any product in general, but it is especially true for Open Source Software (OSS), whose trustworthiness is sometimes still regarded as not as guaranteed as that of closed source products. Trustworthiness is a major issue when people and organizations are faced with the selection and the adoption of new software. Although some ad-hoc methods have been proposed, there is not yet general agreement about which software characteristics contribute to trustworthiness. Therefore, this work focuses on defining an adequate notion of trustworthiness of Open Source products and artifacts and identifying a number of factors that influence it to help and guide both developers and users when deciding whether a given program (or library or other piece of software) is "good enough" and can be trusted in order to be used in an industrial or professional context. The result of this work is a set of estimation models for the perceived trustworthiness of OSS.