Stokes space based digital signal processing (DSP) techniques can improve polarization demultiplexing, polarization dependent losses compensation, and other polarization-related tasks in coherent receivers, particularly in terms of convergence speed and transparency to higher-level emph{M}-ary modulated signals. This paper reports recent advances on Stokes space based DSP for coherent optical communications. We study and discuss the performance the polarization demultiplexing algorithm in terms of convergence speed and computational complexity, and present a new space-demultiplexing algorithm based on signal analysis in higher-order Poincaré spheres for spatial division multiplexing transmission systems. Moreover, practical issues regarding the real-time implementation on FPGAs of Stokes space based algorithms for flexible optical communications are also investigated and discussed.