  A detailed study of the Frohlich polaron model is performed on the basis of
diagrammatic quantum Monte Carlo method. The method is further developed both
quantitatively (performance) and qualitatively (new estimators), and is
enhanced by spectral analysis of the polaron Green function, within a novel
approach. We present the best up to date results for the binding energy, and
for the first time make available precise data for the effective mass,
including the region of intermediate and strong couplings. We look at the
structure of the polaron cloud and answer such questions as the average number
of phonons in the cloud and their number/momentum distribution. The spectral
analysis reveals non-trivial structure of the spectral density at intermediate
and large coupling: the spectral continuum features pronounced peaks that we
attribute to unstable excited states of the polaron.
