Reduced Order Modeling (ROM) is of paramount importance for smart monitoring and control of complex systems in multi-scenario contexts, enabling early risk detection and informed data-efficient decision-making. However, conventional ROM strategies are typically limited to known and constant parameters, inefficient for nonlinear and chaotic dynamics, and blind to the actual system behavior. In this work, we propose a sensor-driven Reduced Order Modeling strategy based on SHallow REcurrent Decoder networks (SHRED-ROM). Specifically, motivated by the well-known method of separation of variables, we consider the composition of a Long Short-Term Memory (LSTM), which encodes the temporal dynamics of limited sensor measurements in multiple scenarios, and a shallow decoder, that reconstructs the corresponding high-dimensional spatio-temporal field. To enhance computational efficiency and memory usage, the snapshots dimensionality is reduced by data- or physics-driven basis expansions, allowing for compressive training of the networks with minimal hyperparameter tuning. By employing SHRED-ROM to control problems, it is possible to efficiently retrieve distributed control actions starting from sparse state measurements. Through applications on climate modeling and environmental monitoring, we show that SHRED-ROM (i) accurately reconstructs and controls challenging dynamics in multiple scenarios with minimal sensor requirement, independently on sensor placement, (ii) can cope with both physical, geometrical and time-dependent parametric dependencies, while being agnostic to their actual values, (iii) can accurately estimate unknown parameters, and (iv) can deal with different data sources, such as high-fidelity simulations, coupled fields and videos.