Scenario optimisation has gained significant attention in the control community due to its ability to provide distribution-free guarantees on the optimal solution of convex (and, more recently, non-convex) optimisation problems. At the core of the approach lies the construction of so-called scenario programs, where constraints are enforced for each available sample. Fully supported convex problems constitute the class of scenario programs for which tight bounds on the violation probability are available. In the first part of the talk, I will present recent developments on the sampling-and-discarding scheme for scenario programs and introduce a tight bound on the violation probability for a natural removal algorithm. These developments build on the connection between a-priori scenario programs and compression learning theory. In the second part of the talk, I will build on these results to establish connections between the scenario approach and conformal prediction. We will also show how conformal prediction arguments can be exploited to recover one of the first results concerning the expectation of the violation probability.