In phylogenetics, distinctly leaf-labeled trees are commonly used to represent the evolution of a set of species. The problem of merging several input trees into a single tree is an important problem in this setting, called supertree reconstruction. This talk focuses on a particular formulation of this general problem, known as the Maximum Agreement Supertree problem. We also consider variants of the problem when the input trees are 3-leaf trees, also known as rooted triples. We present simple combinatorial algorithms for these problems, and raise some open questions.