A Steiner triple system STS(v) is a set of triples of {1, 2, . . . , v} such that every pair of points belongs to exactly one of these triples. A Kirkman triple system KTS(v) is a STS(v) whose triples can be partitioned into parallel classes, each of which is a partition of the point set. A KTS(v) is called 3-pyramidal if it admits a group of automorphisms that fixes 3 points and acts regularly on the other points. I will present recent results we obtained about 3-pyramidal Kirkman triple systems. This is joint work with  S. Bonvicini, M. Buratti, G. Rinaldi and T. Traetta.