  We report on the ALPHA Collaboration's lattice B-physics programme based on
N_f=2 O(a) improved Wilson fermions and HQET, including all NLO effects in the
inverse heavy quark mass, as well as non-perturbative renormalization and
matching, to fix the parameters of the effective theory. Our simulations in
large physical volume cover 3 lattice spacings a ~ (0.08-0.05) fm and pion
masses down to 190 MeV to control continuum and chiral extrapolations. We
present the status of results for the b-quark mass and the B_(s)-meson decay
constants, f_B and f_{B_s}.
