In this seminar, we detail results from multiple studies which have utilized data-driven ideologies for tackling the challenging problem of closure in the large eddy simulations (LES) of nonlinear partial differential equations. One motivation for this research is the long-term objective of precluding phenomenological arguments which limit closure generalizability across different flow classes. Our novel data-driven closures are implemented through various artificial neural network formulations trained through data-harvesting from direct numerical simulations. Our analyses are both a-priori and a-posteriori, with the latter representing one of the first implementations of a purely data-driven turbulence closure within the LES paradigm. The performance of our proposed framework is highly promising, with networks showing the ability to learn sub-grid models which compare favorably to a-priori model-form and model-coefficient based eddy-viscosity closures for decaying two and th ree-dimensional turbulence.