To develop a new generation of diagnostics for halitosis, replacing the subjective organoleptic assessment, a series of exhaled breath analyzers has been developed and assessed. All three devices rely on the assessment of exhaled volatile sulfuric compounds (VSCs), which are mainly generated in and emitted from the oral cavity, contributing to the malodor. Portable, on-site and easy to use, these devices have potential for non-invasive diagnosis of halitosis. However, global assessment of exhaled VSCs alone has two main drawbacks: (i) the absence of VSCs does not rule out halitosis; (ii) non-sulfuric volatile compounds that could be biomarkers of systemic diseases, found in up to 15% of halitosis cases, are neglected. In this article, we review and discuss progress to date in the field of oral/exhaled volatile compounds as potential noninvasive diagnostics for halitosis. We will briefly describe the generation of these compounds both from local (oral) and distal (extra-oral) sources. In addition, we debate the different analytical approaches in use and discuss the potential value of bio-inspired artificially intelligent olfaction in diagnosing and classifying oral and systemic diseases by analyzing exhaled breath.