Internet of Bio-Nano Things (IoBNT) is envisioned to be a heterogeneous network of nanoscale and biological devices, so called Bio-Nano Things (BNTs), communicating via non-conventional means, e.g., molecular communications (MC), in non-conventional environments, e.g., inside human body. The main objective of this emerging networking framework is to enable direct and seamless interaction with biological systems for accurate sensing and control of their dynamics in real time. This close interaction between bio and cyber domains with unprecedentedly high spatio-temporal resolution is expected to open up vast opportunities to devise novel applications, especially in healthcare area, such as intrabody continuous health monitoring. There are, however, substantial challenges to be overcome if the enormous potential of the IoBNT is to be realized. These range from developing feasible nanocommunication and energy harvesting techniques for BNTs to handling the big data generated by IoBNT. In this survey, we attempt to provide a comprehensive overview of the IoBNT framework along with its main components and applications. An investigation of key technological challenges is presented together with a detailed review of the state-of-the-art approaches and a discussion of future research directions.