Deep neural networks (DNNs) are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although DNNs involve the composition of simple arithmetic operations, it can be very challenging to verify whether a particular network satisfies certain input-output properties. This work introduces NeuralVerification.jl, a software package that implements methods that have emerged recently for soundly verifying such properties. These methods borrow insights from reachability analysis, optimization, and search. We present the formal problem definition and briefly discuss the fundamental differences between the implemented algorithms. In addition, we provide a pedagogical example of how to use the library.