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.