A wealth of physical phenomena, both at thermal equilibrium and away from it, exhibit anisotropic
scale invariance: distances along one or several principal axes scale as powers of the distances along
the remaining ones. This anisotropy makes such phenomena already in bulk systems much richer
and more challenging to study. All the more so, this applies to boundary critical phenomena in
anisotropic scale invariant systems. For those, the orientation of a boundary plane matters in an
essential way, since the distance from it scales differently, depending on how it is oriented. Critical
phenomena at bulk Lifshitz points - multicritical points, at which a disordered phase meets both
a homogeneous ordered as well as a modulated ordered one - provide important examples of such
systems. Their bulk universality classes are described by natural generalizations of the standard Phi to power 4
n-vector model, whose systematic analysis via modern field-theoretic renormalization group methods
has been a long-standing challenge ever since their introduction in the 1970s. A survey of recent
progress made in this direction for the bulk case is presented. The construction of semi-infinite
minimal Phi to power 4 models representing the universality classes of the various surface transitions at m-axial
bulk Lifshitz points for distinct types of surface orientations is explained. Results obtained mostly
via dimensionality expansions are given and compared with available Monte Carlo and other results.