Modeling practice seems to be partitioned into scientific models defined by mechanistic differential equations and machine learning models defined by parameterizations of neural networks. While the ability for interpretable mechanistic models to extrapolate from little information is seemingly at odds with the big data “model-free” approach of neural networks, the next step in scientific progress is to utilize these methodologies together in order to emphasize their strengths while mitigating weaknesses. In this talk we will describe four separate ways that we are merging differential equations and deep learning through the power of the DifferentialEquations.jl and Flux.jl libraries. Data-driven hypothesis generation of model structure, automated real-time control of dynamical systems, accelerated of PDE solving, and memory-efficient deep learning workflows will all shown to be derived from this common computational structure of differential equations mixed with neural networks (neural ODEs, neural SDE, neural PDEs). The audience will leave with a new appreciation of how these two disciplines can benefit from one another, and how neural networks can be used for more than just data analysis.