  Calculation results for the HQET field anomalous dimension and the QCD cusp
anomalous dimension, as well as their properties, are reviewed. The HQET field
anomalous dimension $\gamma_h$ is known up to 4 loops. The cusp anomalous
dimension $\Gamma(\varphi)$ is known up to 3 loops, and its small-angle and
large-angle asymptotics -- up to 4 loops. Some (but not all) color structures
at 4 loops are known with the full $\varphi$ dependence. Some simple
contributions are known at higher loops. For the $\varphi\to\infty$ asymptotics
of $\Gamma(\varphi)$ (the light-like cusp anomalous dimension) and the
$\varphi^2$ term of the small-$\varphi$ expansion (the Bremsstrahlung
function), the $\mathcal{N}=4$ SYM results are equal to the highest-weight
parts of the QCD results. There is an interesting conjecture about the
structure of $\Gamma(\varphi)$ which holds up to 3 loops; at 4 loops it holds
for some color structures and breaks down for other ones. In cases when it
holds it related highly non-trivial functions of $\varphi$, and it cannot be
accidental; however, the reasons of this conjecture and its failures are not
understood. The cusp anomalous dimension at Euclidean angle $\phi\to\pi$ is
related to the static quark-antiquark potential due to conformal symmetry; in
QCD this relation is broken by an anomalous term proportional to the $\beta$
function.
  Some new results are also presented. Using the recent 4-loop result for
$\gamma_h$, here we obtain analytical expressions for some terms in the 4-loop
on-shell renormalization constant of the massive quark field $Z_Q^{\text{os}}$
which were previously known only numerically. We also present 2 new
contribution to $\gamma_h$, $\Gamma(\varphi)$ at 5 loops and to the
quark-antiquark potential at 4 loops.
