  It is remarkable how the Froehlich polaron, one of the simplest examples of a
Quantum Field Theoretical problem, as it basically consists of a single fermion
interacting with a scalar Bose field of ion displacements, has resisted full
analytical or numerical solution at all coupling since 1950, when its
Hamiltonian was first written. The field has been a testing ground for
analytical, semi-analytical, and numerical techniques, such as path integrals,
strong-coupling perturbation expansion, advanced variational, exact
diagonalisation (ED), and quantum Monte Carlo (QMC) techniques. This article
reviews recent developments in the field of continuum and discrete (lattice)
Froehlich (bi)polarons starting with the basics and covering a number of active
directions of research.
