  The Fr\"ohlich polaron model describes a ubiquitous class of problems
concerned with understanding properties of a single mobile particle interacting
with a bosonic reservoir. Originally introduced in the context of electrons
interacting with phonons in crystals, this model found applications in such
diverse areas as strongly correlated electron systems, quantum information, and
high energy physics. In the last few years this model has been applied to
describe impurity atoms immersed in Bose-Einstein condensates of ultracold
atoms. The tunability of microscopic parameters in ensembles of ultracold atoms
and the rich experimental toolbox of atomic physics should allow to test many
theoretical predictions and give us new insights into equilibrium and dynamical
properties of polarons. In these lecture notes we provide an overview of common
theoretical approaches that have been used to study BEC polarons, including
Rayleigh-Schr\"odinger and Green's function perturbation theories,
self-consistent Born approximation, mean-field approach, Feynman's variational
path integral approach, Monte Carlo simulations, renormalization group
calculations, and Gaussian variational ansatz. We focus on the renormalization
group approach and provide details of analysis that have not been presented in
earlier publications. We show that this method helps to resolve striking
discrepancy in polaron energies obtained using mean-field approximation and
Monte Carlo simulations. We also discuss applications of this method to the
calculation of the effective mass of BEC polarons. As one experimentally
relevant example of a non-equililbrium problem we consider Bloch oscillations
of Bose polarons and demonstrate that one should find considerable deviations
from the commonly accepted phenomenological Esaki-Tsu model. We review which
parameter regimes of Bose polarons can be achieved in various atomic mixtures.
