From using health data for medical research to using location traces for location-based services, the seemingly different applications have one characteristic in common – the data are spatiotemporally correlated. Such correlations, if not modeled and addressed carefully, challenge the utility of traditional differential privacy mechanisms and even the privacy guarantee of standard definitions. For aggregate health data learning and release, I will present case studies of applying differential privacy for deep learning and computational phenotyping using wearable data and Electronic Health Records (EHRs) considering their spatiotemporal characteristics, and a study quantifying privacy leakage of traditional data release mechanisms under spatiotemporal correlations. For individual location-based services, I will present new privacy notions and mechanisms extending traditional differential privacy for location and spatiotemporal event protection under spatiotemporal correlations. I will conclude the talk with a discussion of open challenges.