Sodium is one of the best examples of a free-electron-like metal and of a certain technological interest. However, an unambiguous determination of the structural evolution of sodium clusters is challenging. Here, we performed an unbiased structure search among neutral and anionic sodium clusters in the medium size range of 10-25 atoms, using the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) method. Geometries are determined by CALYPSO structure searches, followed by reoptimization of a large number of candidate structures. For most cluster sizes the simulated photoelectron spectra of the lowest-energy structures are in excellent agreement with the experimental data, indicating that the current ground-state structures are the true minima. The equilibrium geometries show that, for both neutral and anionic species, the structural evolution from bilayer structures to layered outsides with interior atoms occurs at n = 16. A novel unprecedented honeycomb-like structure of Na-20 cluster with C-3 symmetry is uncovered, which is more stable than the prior suggested structure based on pentagonal structural motifs.