  We give an overview of results on critical phenomena in 4 dimensions,
obtained recently using a rigorous renormalisation group method. In particular,
for the $n$-component $|\varphi|^4$ spin model in dimension 4, with small
coupling constant, we prove that the susceptibility diverges with a logarithmic
correction to the mean-field behaviour with exponent $(n+2)/(n+8)$. This result
extends rigorously to $n=0$, interpreted as a supersymmetric version of the
model that represents exactly the continuous-time weakly self-avoiding walk. We
also analyse the critical two-point function of the weakly self-avoiding walk,
the specific heat and pressure of the $|\varphi|^4$ model, as well as scaling
limits of the spin field close to the critical point.
