Rapid advances in cuffless blood pressure (BP) monitoring over the last decade have the potential to radically transform cardiovascular healthcare. In this two-part review, we first provide a tutorial on the technology behind cuffless BP monitoring, delving into (i) sensors and systems, (ii) pre-processing and feature extraction, and (iii) estimation algorithms. We systematically review the state-of-the-art methods. We found large heterogeneity in study design, data leakage, and underpowered studies, making reliable quantitative comparisons across devices and algorithms challenging. To standardize this, we provide an open-contribution benchmark. We observe that dataset distribution is a significant confounder in error. We suggest using ”explained deviation” to account for systematic variations across studies. We identify that the time between calibration and test is an important confounder in personalized devices. Finally, we complement this review paper with a website, https://wearablebp.github.io, providing a timely platform to understand the state of wearable BP.