Abstract : Experimental mathematics can be roughly described as a 3-step process: compute a high-order approximation of the solution, guess/conjecture a general pattern, prove the conjecture. The technique of guessing can be very fruitful when dealing, for example, with recurrent sequences which arise in practice. This holds true especially when guessing is performed algorithmically and efficiently. In the talk I will explain some algorithmic tools for guessing and illustrate them on examples from own recent mathematical research. Parts of this talk are based on joint work with Alin Bostan and Jacques-Arthur Weil.