We study the dynamics of ultracold atoms in an optical lattice under consta
nt bias. After recapitulating the ideas underlying Bloch oscillations and Z
ener's formula for interband transitions, the Bloch-Zener scenario is teste
d by means of accurate numerical solutions to the time-dependent Schrodinge
r equation. It is shown how two shortcomings of the traditional Zener formu
la can be removed: the common weak-binding approximation can be circumvente
d by combining Kohn's insight into the structure of complex energy bands wi
th the Dykhne-Davis-Pechukas description of transitions in terms of adiabat
ic excursions on analytically continued eigenvalue surfaces, and a usually
neglected Stokes phenomenon comes into play when accounting for the finite
width of the Brillouin zone. Treating Bose-Einstein condensates in optical
lattices within the standard mean-field approximation at zero temperature,
the ideal Bloch-Zener scenario turns out to be remarkably stable against th
e condensate's nonlinear self-interaction. Yet, under appropriate condition
s a Bloch-oscillating Gross-Pitaevskii wavepacket reveals characteristic si
gnatures of that nonlinearity, such as sudden phase jumps, slight shifts of
the oscillation frequency or non-classical breathing modes. It is suggeste
d that such experimentally detectable signatures will play an important rol
e in future high-precision experiments aiming at the exploration of many-bo
dy dynamics in periodic potentials with condensates in optical lattices.