  We provide a detailed presentation of the functional renormalisation group
(FRG) approach for weakly-interacting Bose-Bose mixtures, including a complete
discussion on the RG equations. To test this approach, we examine thermodynamic
properties of balanced three-dimensional Bose-Bose gases at zero and finite
temperatures and find a good agreement with related works. We also study
ground-state energies of repulsive Bose polarons by examining mixtures in the
limit of infinite population imbalance. Finally, we discuss future applications
of the FRG to novel problems in Bose-Bose mixtures and related systems.
