Very complex systems occur nowadays quite frequently in many technological areas and they are often required to comply with high dependability standards. To study their availability and reliability characteristics, Markovian models are commonly used. Due to the size and complexity of the systems, and due to the rarity of system failures, both analytical solutions and “crude” simulations can be inefficient or even non-relevant. A number of variance reduction Monte Carlo techniques have been proposed to overcome this difficulty; importance sampling methods are among the most efficient. The objective of this paper is to survey existing importance sampling schemes, to propose some new schemes and improvements on existing ones, and to discuss their different properties.