  This work discusses charmless inclusive B decays and their application to the
extraction of $|V_{ub}|$. Starting from first principles we relate the
differential decay rate to the hadronic tensor in terms of optimal choice of
kinematical variables. We review the traditional methods of calculating the
hadronic tensor, expansion in $\alpha_s$ and HQET, and discuss their
shortcomings. In the kinematical region relevant for experiment ("shape
function" region), the hadronic tensor can be factorized, at each order in
$1/m_b$, as a product of calculable hard functions and a convolution of
calculable jet functions with non perturbative shape functions. Using SCET, we
calculate the leading order hard and jet function to first order in $\alpha_s$.
Large logarithms are resummed in RGE improved perturbation theory. Local OPE is
used to relate moments of the renormalized shape function to HQET parameters,
defined in the "shape function scheme". Beyond leading order in $1/m_b$,
several subleading shape functions arise. We derive them at tree level, where
they can be expressed as forward matrix elements of bi-local light-cone
operators. Based on these theoretical calculations we present two applications.
In the first, we present the "state-of-the-art " expressions for the triple
differential $\bar B\to X_u l\bar\nu$ decay rate and the $\bar B\to X_s\gamma$
photon spectrum. These expressions include all known contributions and smoothly
interpolate between the "shape-function" and "OPE region". Based on these an
event generator can be constructed, from which the theoretical prediction for
any experimental cut can be extracted. In the second, a weight function is
constructed that relates the $P_+$ spectrum in $\bar B\to X_u l\bar\nu$ to the
normalized $\bar B\to X_s\gamma$ photon spectrum.
