Humankind mimics the processes and strategies that nature has perfected and uses them as a model to address its problems. That has recently found a new direction, i.e., a novel communication technology called molecular communication (MC), using molecules to encode, transmit, and receive information. Despite extensive research, an innate MC method with plenty of natural instances, i.e., olfactory or odor communication, has not yet been studied with the tools of information and communication technologies (ICT). Existing studies focus on digitizing this sense and developing actuators without inspecting the principles of odor-based information coding and MC, which significantly limits its application potential. Hence, there is a need to focus cross-disciplinary research efforts to reveal the fundamentals of this unconventional communication modality from an ICT perspective. The ways of natural odor MC in nature need to be anatomized and engineered for end-to-end communication among humans and human-made things to enable several multi-sense augmented reality technologies reinforced with olfactory senses for novel applications and solutions in the Internet of Everything (IoE). This paper introduces the concept of odor-based molecular communication (OMC) and provides a comprehensive examination of olfactory systems. It explores odor communication in nature, including aspects of odor information, channels, reception, spatial perception, and cognitive functions. Additionally, a comprehensive comparison of various communication systems sets the foundation for further investigation. By highlighting the unique characteristics, advantages, and potential applications of OMC through this comparative analysis, the paper lays the groundwork for exploring the modeling of an end-to-end OMC channel, considering the design of OMC transmitters and receivers, and developing innovative OMC techniques.