Advances in synthetic biology and nanotechnology have contributed to the design of tools that can be used to control, reuse, modify, and re-engineer cells' structure, as well as enabling engineers to effectively use biological cells as programmable substrates to realize Bio-Nano Things (biological embedded computing devices). Bio-NanoThings are generally tiny, non-intrusive, and concealable devices that can be used for in-vivo applications such as intra-body sensing and actuation networks, where the use of artificial devices can be detrimental. Such (nano-scale) devices can be used in various healthcare settings such as continuous health monitoring, targeted drug delivery, and nano-surgeries. These services can also be grouped to form a collaborative network (i.e., nanonetwork), whose performance can potentially be improved when connected to higher bandwidth external networks such as the Internet, say via 5G. However, to realize the IoBNT paradigm, it is also important to seamlessly connect the biological environment with the technological landscape by having a dynamic interface design to convert biochemical signals from the human body into an equivalent electromagnetic signal (and vice versa). This, unfortunately, risks the exposure of internal biological mechanisms to cyber-based sensing and medical actuation, with potential security and privacy implications. This paper comprehensively reviews bio-cyber interface for IoBNT architecture, focusing on bio-cyber interfacing options for IoBNT like biologically inspired bio-electronic devices, RFID enabled implantable chips, and electronic tattoos. This study also identifies known and potential security and privacy vulnerabilities and mitigation strategies for consideration in future IoBNT designs and implementations.