A series of recent model studies and experiments has shown that a variety of different spiral waves can form in two-dimensional complex oscillatory media. It is found that `line-defects' -- dynamic defects having shapes of line -- underlie the morphologies and temporal evolutions of these waves. In this talk, I will review various instabilities associated with the line-defects based on model studies (using Williamowski-R\"ossler reaction-diffusion system) as well as experiments on a Belousov-Zhabotinsky reaction-diffusion system. Discussions will be focused on 1) emergence of a period-2 (P-2) spiral wave, 2) meandering of the line-defect associated with a P-2 spiral wave, 3) transverse instability of a line-defect and line-defect mediated spatio-temporal chaos, and 4) complex wave dynamics in an in-vitro cardiac system.