\section{Introduction}
\subsection{Overview}
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The standard model (SM) of elementary particle physics \cite{GSW-Model}
has turned out
to be a overwhelmingly successful description of the phenomena in 
high energy physics. Certain aspects of it, namely the couplings of the 
quarks and leptons to the neutral weak boson, have been tested with
very high precision and confirmed the SM even at the level of loop 
corrections. 

Despite of this success many people are convinced that the SM cannot 
be the final theory. In particular the Higgs sector is not considered 
satisfactory, since one of its main ingredients, 
the neutral scalar Higgs boson has not yet been seen. Related to the 
structure of the Higgs sector is the way the quarks and leptons acquire 
their masses and the mixing of quark flavours, parametrized by a 
$3 \times 3$ unitary matrix, the so-called Cabibbo Kobayashi Maskawa
(CKM) matrix \cite{CKM-matrix}. 

The CKM matrix in the SM encodes also the effect of CP violation which 
has been observed up to now only in the system of neutral $K$ mesons.
Alternative models, such as the superweak model proposed by Wolfenstein
\cite{SuperWeak}
have been formulated and have not yet been ruled out definitively. 
In other words, the CKM sector of the SM has not been tested at a 
level of precision that can be compared to what is known about the 
$Z_0$ couplings form the LEP experiments.

In order to test this part of the SM one has to study charged current
or flavour changing neutral current (FCNC) processes of quarks. The 
SM makes predictions for the processes involving quarks, however, 
experimentally only hadrons are observable. In order to connect the 
parameters of the SM with the data one has to deal with the bound
state problem of strong interactions, which has not yet been solved 
starting form the fundamental entities of QCD, with the possible 
exception of lattice gauge theory which recently has produced first 
results on weak form factors \cite{Lattice}. 

In the past five years considerable progress has been made towards 
a QCD-based and model independent description of hadrons containing 
a heavy-flavour quark, where heavy means that the mass of the quark $m_Q$ 
is large compared to some scale $\bar\Lambda$ determined by the light 
degrees of freedom, e.g. the constituent quark mass of a light quark
or the scale $\Lambda_{QCD}$ entering through the running of the strong 
coupling $\alpha_s$.  
This progress has been achieved by the use of 
the heavy mass limit for the heavy quark, in which it is replaced by 
a static source of a colour field. This limit of QCD leads to a 
well-defined field theory, the so-called Heavy Quark Effective Theory (HQET).

The infinite mass limit from QCD has been known for some time 
\cite{shifman}, but the main observation, which triggered the 
enormous development of this field, is that in the infinite mass limit
two additional symmetries appear which are not present in full QCD 
\cite{isgur/wise}. Since then the implications of the heavy mass limit 
and HQET have been extensively studied in innumerable publications, and 
the development of the field is documented in more or less extensive 
reviews \cite{reviews}.

The two additional symmetries of the heavy mass limit have important 
phenomenological applications; they lead to model-independent 
relations between 
form factors describing e.g. exclusive weak decays. The origin of 
the new symmetries 
is quite simple. The first symmetry is a heavy-flavour symmetry, which is 
due to the fact that the interaction of the quarks with 
the gluons is flavour-blind and in the heavy mass limit all heavy quarks 
act as a static source of colour. Formally this corresponds to an $SU(2)$
symmetry relating $b$ and $c$ quarks moving with the same velocity.  
The second symmetry is the spin symmetry of the heavy quark. 
The interaction of the heavy quark spin with 
the ``chromomagnetic'' field is inversely proportional to the heavy mass
and hence vanishes in the infinite mass limit. As a consequence, the 
rotations for the heavy quark spin become an $SU(2)$ symmetry, which 
holds for a fixed velocity of the heavy quark. 

Corrections to the limit $m_Q \to \infty$ may be studied systematically
in the framework of HQET. The corrections
are given as power series expansions in two small parameters. The
first small parameter is the strong coupling constant,
taken at the scale of the heavy quark $\alpha_s (m_Q)$. This type
of correction may be calculated systematically using perturbation
theory in HQET. 
The second type of correction is characterized by the small parameter
$\bar\Lambda / m_Q$, where $\bar\Lambda$ is a scale of 
the light QCD degrees of freedom, e.g. $\bar\Lambda \sim m_{hadron}-m_Q$.
In the effective theory approach this type of corrections enter 
through operators of higher dimension,
the matrix elements of which have to be parametrized in general
by additional form factors.

More or less parallel to the development of heavy quark symmetry and 
HQET, which is well suited for exclusive decays, the heavy mass expansion 
has been applied also to inclusive decays \cite{Manifesto}-\cite{FLS93}.
The heavy quark mass 
sets a scale that is large compared to $\Lambda_{QCD}$, 
and one may use a similar
setup as in deep inelastic scattering for the inclusive decays; in 
particular, the operator product expansion for the inclusive decays
yields an expansion in inverse powers of the heavy quark mass. In this
way one may not only study total rates, but also differential distributions
such as the lepton energy spectra in inclusive semileptonic decays. 

This theoretical progress has a large impact on the determination 
of the CKM matrix, in particular on the matrix elements $V_{ub}$ 
and $V_{cb}$. In the near future these entries will be measured from 
semileptonic $B$ decays with at least controllable theoretical 
uncertainties, since the $1/m_Q$ expansion makes definite predictions
and the uncertainties may be estimated in the framework of the $1/m_Q$ 
expansion and QCD perturbation theory. This is a considerable progress 
compared to a few years ago, since the QCD bound state problem had 
to be modelled, and in this way uncontrollable systematic uncertainties
entered the game.  

This review is intended to summarize the development over the past 
few years of heavy mass expansion methods based on QCD. The first 
part is devoted to the theoretical framework and its basis in QCD. 
The second part deals with applications, in particular with the 
possibility to extract CKM matrix elements form heavy flavour decays. 
Finally, the application of the $1/m_Q$ expansion to inclusive decays
is consiedered and the lifetimes of heavy hadrons are considered in 
this framework.      

