  According to recent results, the Gell-Mann - Low function \beta(g) of
four-dimensional \phi^4 theory is non-alternating and has a linear asymptotics
at infinity. According to the Bogoliubov and Shirkov classification, it means
possibility to construct the continuous theory with finite interaction at large
distances. This conclusion is in visible contradiction with the lattice results
indicating triviality of \phi^4 theory. This contradiction is resolved by a
special character of renormalizability in \phi^4 theory: to obtain the
continuous renormalized theory, there is no need to eliminate a lattice from
the bare theory. In fact, such kind of renormalizability is not accidental and
can be understood in the framework of Wilson's many-parameter renormalization
group. Application of these ideas to QCD shows that Wilson's theory of
confinement is not purely illustrative, but has a direct relation to a real
situation. As a result, the problem of analytical proof of confinement and a
mass gap can be considered as solved, at least on the physical level of rigor.
