In this article, we present current methodologies, available technologies, and demands for monitoring various respiratory parameters. We discuss the importance of noninvasive techniques for remote and continuous monitoring and challenges involved in the current "smart and connected health" era. We conducted an extensive literature review on the medical significance of monitoring respiratory vital parameters, along with the current methods and solutions with their respective advantages and disadvantages. We discuss the challenges of developing a noninvasive, wearable, wireless system that continuously monitors respiration parameters and opportunities in the field and then determine the requirements of a state-of-the-art system. Noninvasive techniques provide a significant amount of medical information for a continuous patient monitoring system. Contact methods offer more advantages than non-contact methods; however, reducing the size and power of contact methods is critical for enabling a wearable, wireless medical monitoring system. Continuous and accurate remote monitoring, along with other physiological data, can help caregivers improve the quality of care and allow patients greater freedom outside the hospital. Such monitoring systems could lead to highly tailored treatment plans, shorten patient stays at medical facilities, and reduce the cost of treatment.