  We discuss theoretical and phenomenological aspects of two-Higgs-doublet
extensions of the Standard Model. In general, these extensions have scalar
mediated flavour changing neutral currents which are strongly constrained by
experiment. Various strategies are discussed to control these flavour changing
scalar currents and their phenomenological consequences are analysed. In
particular, scenarios with natural flavour conservation are investigated,
including the so-called type I and type II models as well as lepton-specific
and inert models. Type III models are then discussed, where scalar flavour
changing neutral currents are present at tree level, but are suppressed by
either specific ansatze for the Yukawa couplings or by the introduction of
family symmetries. We also consider the phenomenology of charged scalars in
these models. Next we turn to the role of symmetries in the scalar sector. We
discuss the six symmetry-constrained scalar potentials and their extension into
the fermion sector. The vacuum structure of the scalar potential is analysed,
including a study of the vacuum stability conditions on the potential and its
renormalization-group improvement. The stability of the tree level minimum of
the scalar potential in connection with electric charge conservation and its
behaviour under CP is analysed. The question of CP violation is addressed in
detail, including the cases of explicit CP violation and spontaneous CP
violation. We present a detailed study of weak basis invariants which are odd
under CP. A careful study of spontaneous CP violation is presented, including
an analysis of the conditions which have to be satisfied in order for a vacuum
to violate CP. We present minimal models of CP violation where the vacuum phase
is sufficient to generate a complex CKM matrix, which is at present a
requirement for any realistic model of spontaneous CP violation.
