With the widespread use of smartphones and wearable health sensors, a plethora of mobile health (mHealth) applications to track well-being, run human behavioral studies, and clinical trials have emerged in recent years. However, the design, development, and deployment of mHealth applications is challenging in many ways. To address these challenges, several generic mobile sensing frameworks have been researched in the past decade. Such frameworks assist developers and researchers in reducing the complexity, time, and cost required to build and deploy health-sensing applications. The main goal of this article is to provide the reader with an overview of the state-of-the-art of health-focused generic mobile and wearable sensing frameworks. This review gives a detailed analysis of functional and non-functional features of existing frameworks, the health studies they were used in, and the stakeholders they support. Additionally, we also analyze the historical evolution, uptake, and maintenance after the initial release. Based on this analysis, we suggest new features and opportunities for future generic mHealth sensing frameworks.