Conical intersections (CI) are regions of the potential energy landscape of a chemical system where two or more energy surfaces cross and the quantum levels are degenerate. They have an interesting topological structure, and their existence is signalled by particular geometric properties (the concept of \"Berry phase\" was introduced in this framework). Indeed, the importance of CIs has grown in the last years in the field of photochemistry, since they can represent a very fast reaction channel for the decay of a photochemically excited system. An efficient exploration of these gapless regions can help both in interpreting the experimental data and in suggesting new reaction mechanisms. To this end, we have developed a strategy based upon the methods of constrained molecular dynamics and the variational principles of classical mechanics. This strategy, coupled with high accuracy quantum chemistry schemes, will be discussed in this seminar, together with possible applications to realistic systems.