Dynamical models play a crucial role for understanding and solving problems in many engineering applications or natural systems. In turbulence, weather modeling, chemical processes, and other interesting areas in engineering it is desired to find reduced-order models that can make time predictions. The nature of high-dimensionality in fluid systems and recent advances in machine learning have pushed the boundaries of what can be learned when data and physical knowledge of a system is available. The objective of this thesis is to develop deep learning architectures to learn efficient reduced-order models that can faithfully capture the most important features of flows in a low-dimensional representation. We leverage the use of autoencoders to learn low-dimensional representations and dense neural networks to learn an evolution equation on this low-dimensional space. By enforcing symmetry constraints that appear in the Navier-Stokes equations we show how more accurate models for time prediction can be learned, while reducing significantly the dataset. Finally, we present a framework capable of giving estimates of the minimal dimensions needed to represent systems featuring complex dynamics and intricate behavior.