Discovering high-dimensional spatio-temporal patterns in parametric contexts is an ubiquitous, yet extremely challenging, task in many contexts arising from Applied Sciences and Engineering. Whenever relying on high-fidelity, full-order data, suitable dimensionality reduction strategies are required to find a latent space where the discovery task can be more easily tackled. On the other hand, if only limited sensor measurements are available, a sensing problem has to be solved. When considering parametric contexts, both {\em discovery} and {\em sensing} share several useful building blocks, ultimately supporting full-state estimates of a system (system identification), control decisions and forecasting. In this talk we will discuss a series of strategies recently introduced to accomplish these tasks. Motivated by the need of building reduced order models of parametrized dynamical systems, we will present a data-driven framework which combines dimensionality reduction with reduced dynamics identification through parametric sparse identification of nonlinear dynamics (SINDy). Then, we will briefly outline a recent extension towards uncertainty quantification (UQ) including a variational version of SINDy (VINDy). Featuring an explicit and parametrized modeling of the reduced dynamics, the overall framework presents remarkable capabilities to generalize with respect to both time and parameters. To cope with the case of unknown and nonconstant parameters, as well as observational data and highly nonlinear dynamics, we consider a SHallow REcurrent Decoder-based Reduced Order Modeling technique (SHRED-ROM) capable of reconstructing high-dimensional state dynamics in multiple scenarios from the temporal history of limited sensor measurements. Through several applications, we show that SHRED-ROM is a robust decoding-only strategy, capable of dealing with both fixed or mobile sensors, physical and geometrical parametric dependencies and different data sources, such as high-fidelity simulations, coupled fields, and videos, while being agnostic to sensor placement and parameter values. Finally, further extensions of the SHRED framework including forecast at future times, optimal control, and UQ will also be discussed.