  Polaron quasiparticles are formed when a mobile impurity is coupled to the
elementary excitations of a many-particle background. In the field of ultracold
atoms, the study of the associated impurity problem has attracted a growing
interest over the last fifteen years. Polaron quasiparticle properties are
essential to our understanding of a variety of paradigmatic quantum many-body
systems realized in ultracold atomic gases and in the solid state, from
imbalanced Bose-Fermi and Fermi-Fermi mixtures to fermionic Hubbard models. In
this topical review, we focus on the so-called repulsive polaron branch, which
emerges as an excited many-body state in systems with underlying attractive
interactions such as ultracold atomic mixtures, and is characterized by an
effective repulsion between the impurity and the surrounding medium. We give a
brief account of the current theoretical and experimental understanding of
repulsive polaron properties, for impurities embedded in both fermionic and
bosonic media, and we highlight open issues deserving future investigations.
