In the recent years, Bridgeland stability conditions (BSC for short) have seen a fast development and an increasing interest, mainly for their versatility between category theory, algebraic geometry and theoretical physics. They were introduced by Tom Bridgeland, who was motivated by the work of M.R. Douglas on \Pi-stability in string theory.

During this talk, I shall give a general overview of the notion of BSC explaining their relations to the different fields of mathematics, then mention some examples of their application.

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