In many typical situations, the countable universal homogeneous model of some first-order theory has the property that its automorphism group contains a homeomorphic copy of the automorphism group of each countable model of the theory. In the uncountable case, the analogous statement is typically false. However, there are some situations when the automorphism group of an uncountable homogeneous structure is universal (as a topological group) for the class of automorphism groups of some carefully chosen structures. I would like to present three such examples -- two from the realm of linear orders, and one from the theory of Boolean algebras.