We highlight some recent results on the theory and algorithms for  MIMO systems, obtained at the Royal Institute of  Technology (KTH) within the SATURN project.   The paper includes a a new approximate expression for the ergodic  channel capacity of a MIMO system with correlated fading, algorithms  for MIMO beamforming under EIRP (equivalent isotropic radiated  power) constraints and a low-complexity algorithm for MIMO channel  estimation in OFDM systems. Also, we show how transmit and  beamformers can be determined in a decentralized fashion without  explicitly estimating the channel response.