Wearable sensors are de facto revolutionizing the assessment of standing balance. The aim of this work is to review the state-of-the-art literature that adopts this new posturographic paradigm, i.e., to analyse human postural sway through inertial sensors directly worn on the subject body. After a systematic search on PubMed and Scopus databases, two raters evaluated the quality of 73 full-text articles, selecting 47 high-quality contributions. A good inter-rater reliability was obtained (Cohen’s kappa = 0.79). This selection of papers was used to summarize the available knowledge on the types of sensors used and their positioning, the data acquisition protocols and the main applications in this field (e.g., “active aging”, biofeedback-based rehabilitation for fall prevention, and the management of Parkinson’s disease and other balance-related pathologies), as well as the most adopted outcome measures. A critical discussion on the validation of wearable systems against gold standards is also presented.