I will describe an approach to implementing classical topological field theories in the framework of extended TQFTs using higher categories of iterated spans. In the simplest version, which will be the main focus of the talk, these are arbitrary spans in some (infinity-)category, but I will also mention variants using derived stacks and either symplectic structures and iterated Lagrangian correspondences, or Poisson structures and iterated coisotropic correspondences. The latter was set up in joint work with V. Melani and P. Safronov, and the former is developed in an ongoing project with D. Calaque and C. Scheimbauer.