Abstract: The goal of Numerical Algebraic Geometry is to carry out algebraic geometric calculations in characteristic zero using numerical analysis algorithms. This comes down to numerical algorithms to compute and manipulate solution sets of polynomial systems. Numerical Algebraic Geometry is a natural outgrowth of the continuation methods to compute isolated complex solutions of systems of polynomials with complex coefficients. There are a wide range of applications including solution of chemical systems, kinematics, numerical solution of systems of nonlinear differential equations, and computation of algebraic geometric invariants. Bertini is open-source C software, developed by Bates (Colorado State U.), Hauenstein (Notre Dame), Sommese (Notre Dame), and Wampler (General Motors R. & D.), to carry out Numerical Algebraic Geometry computations. Bertini will be rewritten to make it a better tool for users. Bertini dates from over a decade ago, and from this experience we have identified several possibilities for significant improvements. One goal is to change some of the data structures and add internal functionality that will give the user the ability to write scripts and interface with other software. In this talk, I will give an overview of Numerical Algebraic Geometry with an especial focus on applications to the numerical solution of systems of nonlinear differential equations. I will consider the theoretical algorithms underlying the area in the light of the practical issues that arise when implementing the algorithms in the current and the future Bertini.