Spatio-temporal processes are ubiquitous and prevalent across disciplines. Understanding the mechanisms underlying processes and integrating this information into models is of great interest, as it can improve forecasting accuracy and align with scientific motivation. Examples of such models include Partial Differential Equation (PDE) Models or Physics-Informed Neural Network Models in the applied mathematics or deep learning community, respectively. However, these models often overlook uncertainty quantification despite its crucial role, considering that real-world processes necessarily involve inherent errors that physical laws cannot fully explain. Dynamic Spatio-Temporal Models (DSTMs) offer a flexible and effective approach by embedding physics laws within the Bayesian Hierarchical Model (BHM) framework and accounting for dependencies in space and time conditionally. This dissertation explores integrating physics laws while accounting for uncertainty within BHMs and neural network models for complex environmental processes. To start, a novel approach utilizing a level-set method and low-rank representation within a BHM is developed to model the evolution of wildfire boundaries in the presence of uncertainty in data and a lack of knowledge about the boundaries. Subsequently, a hybrid model that nests an echo state network within a level-set method to accommodate nonlinearity is developed. This model is computationally efficient and includes calibrated uncertainty quantification. Lastly, a new class of DSTMs, capable of accommodating both high and low extremes through a regime-switching scheme of stable distributions with varying tail indices, is presented. This last method is illustrated on fine particulate matter (PM2.5) observations emanating from wildfires in the prairie region of the US. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]