To face the explosion of the Internet traffic, a new generation of optical networks is being developed; the Elastic optical Networks (EONs). The aim with EONs is to use the optical spectrum efficiently and flexibly. The benefit of the flexibility is, however, accompanied by more difficulty in the resource allocation problems. In this report, we study the problem of Spectrum Allocation in Elastic Optical Tree-Networks. In trees, even though the routing is fixed, the spectrum allocation is NP-hard. We survey the complexity and approximability results that have been established for the SA in trees and prove new results for stars and binary trees.