Over the last few decades, sustainable computing has been widely used in areas like social computing, artificial intelligence-based agent systems, mobile computing, and Internet of Things (IoT). There are social, economic, and commercial impacts of IoT on human lives. However, IoT nodes are generally power-constrained with data transmission using an open channel, i.e., Internet which opens the gates for various types of attacks on them. In this context, several efforts are initiated to deal with the evolving security issues in IoT systems and make them self-sufficient to harvest energy for smooth functioning. Motivated by these facts, in this paper, we explore the evolving vulnerabilities in IoT devices. We provide a state-of-the-art survey that addresses multiple dimensions of the IoT realm. Moreover, we provide a general overview of IoT, Sustainable IoT, its architecture, and the Internet Engineering Task Force (IETF) protocol suite. Subsequently, we explore the open-source tools and datasets for the proliferation in research and growth of IoT. A detailed taxonomy of attacks associated with various vulnerabilities is also presented in the text. Then we have specifically focused on the IoT Vulnerability Assessment techniques followed by a case study on sustainability of Smart Agriculture. Finally, this paper outlines the emerging challenges related to IoT and its sustainability, and opening the doors for the beginners to start research in this promising area.