  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.

Quantum Gases;Strongly Correlated Electrons;Atomic Physics