Magnetohydrodynamic (MHD) oscillatory processes in di�erent plasma systems, such as the corona of the Sun and the Earth's magnetosphere show interesting similarities and di�erences, which so far received little attention and remain underexploited. The successful commissioning within the past ten years of SDO, Hinode, STEREO and THEMIS spacecraft, in combination with matured analysis of data from earlier spacecraft (Wind, SOHO, ACE, Cluster, TRACE and RHESSI) makes it very timely to survey the breadth of observations giving evidence for MHD oscillatory processes in solar and space plasmas, and state-of-the-art theoretical modelling. The paper reviews several important topics, such as Alfv�enic resonances and mode conversion; MHD waveguides, such as the magnetotail, coronal loops, coronal streamers; mechanisms
for periodicities produced in energy releases during substorms and solar flares, possibility of Alfv�enic resonators along open �eld lines; possible drivers of MHD waves; diagnostics of plasmas with MHD waves; interaction of MHD waves with partly-ionised boundaries (ionosphere and chromosphere). The review is mainly oriented to specialists
in magnetospheric physics and solar physics, but not familiar with speci�cs of the adjacent research �elds
