The next generation of the Internet of Things (IoT) facilitates the integration of the notion of social networking into smart objects (i.e., things) in a bid to establish the social network of interconnected objects. This integration has led to the evolution of a promising and emerging paradigm of Social Internet of Things (SIoT), wherein the smart objects act as social objects and intelligently impersonate the social behaviour similar to that of humans. These social objects are capable of establishing social relationships with the other objects in the network and can utilize these relationships for service discovery. Trust plays a significant role to achieve the common goal of trustworthy collaboration and cooperation among the objects and provide systems' credibility and reliability. In SIoT, an untrustworthy object can disrupt the basic functionality of a service by delivering malicious messages and adversely affect the quality and reliability of the service. In this survey, we present a holistic view of trustworthiness management for SIoT. The essence of trust in various disciplines has been discussed along with the Trust in SIoT followed by a detailed study on trust management components in SIoT. Furthermore, we analyzed and compared the trust management schemes by primarily categorizing them into four groups in terms of their strengths, limitations, trust management components employed in each of the referred trust management schemes, and the performance of these studies vis-a-vis numerous trust evaluation dimensions. Finally, we have discussed the future research directions of the emerging paradigm of SIoT, particularly for trustworthiness management in SIoT.