This work establishes COMPRA, a compact and reactive autonomy framework for fast deployment of Micro Aerial Vehicles (MAVs) in subterranean Search-and-Rescue (SAR) missions. A COMPRA-enabled MAV is able to autonomously explore previously unknown areas while specific mission criteria are considered e.g. an object of interest is identified and localized, the remaining useful battery life, the overall desired exploration mission duration. The proposed architecture follows a low-complexity algorithmic design to facilitate fully on-board computations, including nonlinear control, state-estimation, navigation, exploration behavior and object localization capabilities. The framework is mainly structured around a reactive local avoidance planner, based on enhanced Potential Field concepts and using instantaneous 3D pointclouds, as well as a computationally efficient heading regulation technique, based on depth images from an instantaneous camera stream. Those techniques decouple the collision-free path generation from the dependency of a global map and are capable of handling imprecise localization occasions. Field experimental verification of the overall architecture is performed in relevant unknown Global Positioning System (GPS)-denied environments.