The demand for wearable devices to measure respiratory activity is constantly growing, finding applications in a wide range of scenarios (e.g., clinical environments and workplaces, outdoors for monitoring sports activities, etc.). Particularly, the respiration rate (RR) is a vital parameter since it indicates serious illness (e.g., pneumonia, emphysema, pulmonary embolism, etc.). Therefore, several solutions have been presented in the scientific literature and on the market to make RR monitoring simple, accurate, reliable and noninvasive. Among the different transduction methods, the piezoresistive and inertial ones satisfactorily meet the requirements for smart wearable devices since unobtrusive, lightweight and easy to integrate. Hence, this review paper focuses on innovative wearable devices, detection strategies and algorithms that exploit piezoresistive or inertial sensors to monitor the breathing parameters. At first, this paper presents a comprehensive overview of innovative piezoresistive wearable devices for measuring user’s respiratory variables. Later, a survey of novel piezoresistive textiles to develop wearable devices for detecting breathing movements is reported. Afterwards, the state-of-art about wearable devices to monitor the respiratory parameters, based on inertial sensors (i.e., accelerometers and gyroscopes), is presented for detecting dysfunctions or pathologies in a non-invasive and accurate way. In this field, several processing tools are employed to extract the respiratory parameters from inertial data; therefore, an overview of algorithms and methods to determine the respiratory rate from acceleration data is provided. Finally, comparative analysis for all the covered topics are reported, providing useful insights to develop the next generation of wearable sensors for monitoring respiratory parameters.