Abstract: In 1944, Landau discovered a three-parameter family of explicit (-1)-homogeneous solutions of 3D stationary incompressible Navier-Stokes equations (NSE) with precisely one singularity at the origin. These solutions, now called Landau solutions, are axisymmetric and has no swirl. In 1998 Tian and Xin proved that all (-1)-homogeneous axisymmetric solutions with one singularity are Landau solutions. In 2006 Sverak proved that all (-1)-homogeneous solutions smooth on the unit sphere must be Landau solutions. This talk focuses on (-1)-homogeneous solutions of 3D incompressible stationary NSE with finitely many singular rays. I will first describe some previous results on the existence and classification of such solutions that are axisymmetric with one or two singular rays. We classify all such solutions with no swirl and then obtain existence of nonzero swirl solutions through perturbation methods. I will then discuss the singularity behavior of homogeneous solutions to NSE, and present some recent study on the removable singularity problem for solutions with singular rays. We establish the asymptotic expansion of axisymmetric solutions and obtain an optimal removable singularity result for general homogeneous solutions without the axisymmetry assumption. I will also discuss the asymptotic stability for some solutions we obtained, and talk about some anisotropic Caffarelli-Kohn-Nirenberg type inequalities we derived and applied in the study.