Brownian motion tree models (BMTM) are linear Gaussian covariance models that describe continuous trait evolutions along a phylogenetic tree. The maximum likelihood degree (ML degree) and the reciprocal maximum likelihood degree (RML degree) of a BMTM measure the algebraic complexity of solving the direct and reciprocal maximum likelihood estimation problem, respectively, for these models. We give explicit formulas for the RML degree of any BMTM and present preliminary results on the ML degree of a BMTM. This  includes the invariance of ML degree under the choice of the root in a BMTM and the ML degree of BMTMs with star tree structure. The talk is based on previous work with Boege, Coons, Eur and Rottgers and ongoing work with Coons, Cox and Nometa.