Wearable devices are burgeoning, and applications across numerous verticals are emerging, including human performance monitoring, at-home patient monitoring, and health tracking, to name a few. Off-the-shelf wearables have been developed with focus on portability, usability, and low-cost. As such, when deployed in highly ecological settings, wearable data can be corrupted by artifacts and by missing data, thus severely hampering performance. In this technical note, we overview a signal processing representation called the modulation spectrum. The representation quantifies the rate-of-change of different spectral magnitude components and is shown to separate signal from noise, thus allowing for improved quality measurement, quality enhancement, and noise-robust feature extraction, as well as for disease characterization. We provide an overview of numerous applications developed by the authors over the last decade spanning different wearable modalities and list the results obtained from experimental results alongside comparisons with various state-of-the-art benchmark methods. Open-source software is showcased with the hope that new applications can be developed. We conclude with a discussion on possible future research directions, such as context awareness, signal compression, and improved input representations for deep learning algorithms.