The foundation of algebraic geometry is the problem of solving systems of polynomial equations. Numerical methods can be used to perform algebraic geometric computations forming the field of numerical algebraic geometry which continues to advance rapidly. The continuing progress in computer hardware and software has enabled new algorithms and implementations. Examples include irreducible decompositions in multi-projective spaces, and numerical techniques for computing discrete objects such as polytopes. This session will feature recent progress in algorithms and implementations of theoretical advances in numerical algebraic geometry.