We highlight some recent results on the theory and algorithmsfor MIMO systems, obtained at the Royal Instituteof Technology (KTH) within the SATURN project.The paper includes a a new approximate expression forthe ergodic channel capacity of a MIMO system with correlatedfading, algorithms for MIMO beamforming underEIRP (equivalent isotropic radiated power) constraintsand a low-complexity algorithm for MIMO channel estimationin OFDM systems. Also, we show how transmitand beamformers can be determined in a decentralizedfashion without explicitly estimating the channel response.