Classical biological control (CBC) is the introduction of a natural enemy of exotic origin to control a pest, usually also exotic, aiming at permanent control of the pest. CBC has been carried out widely over a variety of target organisms, but most commonly against insects, using parasitoids and predators and, occasionally, pathogens. Until 2010, 6158 introductions of parasitoids and predators were made against 588 insect pests, leading to the control of 172 pests. About 55% of these introductions were made against pests of woody plants. Establishment rates of natural enemies and success rates were higher in CBC projects targeting pests of woody plants than other pests. This review aims to answer the questions most commonly asked regarding CBC against insect pests, with particular emphasis on tree pests. The topics covered include, among others: variations in rates of successes among different systems, different target insect groups and different agents; temporal trends in CBC practices and successes; economic and environmental benefits; risks and ways to mitigate the risks; CBC against native pests; accidental successes through the adoption of the invasive pests by native natural enemies or accidentally introduced agents; and prospects and constraints for the practice of CBC in the future. Questions are answered based on the analysis of two databases, the BIOCAT2010 database of introductions of insect biological control agents for the CBC of insect pests, and a database of introductions of entomopathogens against insect pests.