  The technique of quantum electrodynamics (QED) calculations of energy levels
in the helium atom is reviewed. The calculations start with the solution of the
Schr\"odinger equation and account for relativistic and QED effects by
perturbation expansion in the fine-structure constant $\alpha$. The
nonrelativistic wave function is represented as a linear combination of basis
functions depending on all three interparticle radial distances, $r_1$, $r_2$
and $r = |\vec{r}_1-\vec{r}_2|$. The choice of the exponential basis functions
of the form $\exp(-\alpha r_1 -\beta r_2 -\gamma r)$ allows us to construct an
accurate and compact representation of the nonrelativistic wave function and to
efficiently compute matrix elements of numerous singular operators representing
relativistic and QED effects. Calculations of the leading QED effects of order
$\alpha^5m$ (where $m$ is the electron mass) are complemented with the
systematic treatment of higher-order $\alpha^6m$ and $\alpha^7m$ QED effects.
