Reduced Order Modeling (ROM) is of paramount importance to efficiently infer full spatio-temporal fields in multi-scenario contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control. 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. To enhance efficiency, several approaches in recent years have exploited tools from scientific machine learning for both (i) the construction of a reduced (or latent) space of low-dimension to express candidate solutions, and (ii) the prediction of the system dynamics for new, unseen scenarios. For instance, deep learning-based ROMs (DL-ROMs) exploit autoencoders to perform dimensionality reduction of snapshots’ data and several options to predict the latent dynamics, ranging from neural networks, to model discovery relying on sparse regression or neural ODEs. In this work, we propose a sensor-driven Reduced Order Modeling (SHRED-ROM) strategy based on SHallow REcurrent Decoder networks. Specifically, we consider the composition of a Long Short-Term Memory (LSTM) network, which encodes the temporal dynamics of few available sensor data in multiple scenarios, and a shallow decoder, that reconstructs the corresponding high-dimensional state .To enhance computational efficiency and memory usage, the dimensionality of full state snapshots is reduced by Proper Orthogonal Decomposition (POD), allowing for compressive networks training with minimal hyperparameter tuning, similarly to the POD-DL-ROM strategy formerly introduced. Through applications on chaotic and nonlinear fluid dynamics, we show that SHRED-ROM (i) accurately estimates both full state dynamics and unknown parameters starting from few sensors in new scenarios, (ii) can deal with both physical and geometrical (possibly time-dependent) parametric dependencies, and (iii) can cope with both fixed and moving sensors, while being agnostic to sensor placement.