In this talk, I will review some results about long time behaviour of linear kinetic equations for which the microscopic equilibrium (that is, the kernel of the reorientation operator) is typically a density with polynomial decay. There will be no space confinement and the reorientation operator could be of scattering, Fokker-Planck or Levy-Fokker-Planck types. I will first present a spectral approach a la Ellis and Pinsky that yields to a unified treatment of the macroscopic limits for this kind of equations and then focus on re-shaping the Dolbeault-Mouhot-Schmeiser L2 hypocoercivity method to get explicit rates of decay to zero in suitable weighted norms. This comes mainly from joint works with Dolbeault, Lafleche and Mouhot.