Buildings are combinatorial and geometric structures that were introduced by Jacques Tits for the study of semi-simple algebraic groups. When a building has the so-called Moufang property, it corresponds to the building having a rich automorphism group. An interesting subgroup of the automorphism group of a Moufang-building is the little projective group, which is the group generated by all root elations. In joined work with Hendrik Van Maldeghem, we found geometrical constructions for root elations of Moufang-buildings of finite diameter that give more insight into their fixpoint structure. We also saw a connection between the little projective groups and the groups of special projectivities of these buildings. At the moment we are working on determining the special and general groups of projectivities for all Moufang-buildings of finite diameter together with Jeroen Schillewaert. In my talk I would like to give some insight into our research, explain what elations and projectivities are and state some group theoretic consequences.