Topological invariants in dynamics such as fixed point index or Conley index found many applications in the qualitative analysis of dynamical systems, in particular existence proofs of stationary and periodic orbits, homoclinic connections and chaotic invariant sets. The classical methods require analytic formulas for vector fields or maps generating the dynamics. This is an obstacle in the case of dynamics known only from samples gathered from observations or experiments. In his seminal work on discrete Morse theory R. Forman showed that a purely combinatorial approach to dynamics is possible. In the talk I'll present an overview of Conley theory in the setting of combinatorial dynamical systems induced by combinatorial (multi)vector fields.