Understanding the physics of the various instabilities and finding their timescales is an important problem in Laboratory and Astrophysical plasmas. Using numerical simulations but mostly analytical work in the linear regime we study their onset in various settings: (i) in the X and Z-pinch experiments in the Centre for Plasma Physics & Lasers, (ii) in AGN and GRB relativistic magnetized jets, (iii) in magnetized accretion disks around Kerr black holes.