  We present upper and lower bounds for Steklov eigenvalues for domains in
$\mathbb{R}^{N+1}$ with $C^2$ boundary compatible with the Weyl asymptotics. In
particular, we obtain sharp upper bounds on Riesz-means and the trace of
corresponding Steklov heat kernel. The key result is a comparison of Steklov
eigenvalues and Laplacian eigenvalues on the boundary of the domain by applying
Pohozaev-type identities on an appropriate tubular neigborhood of the boundary
and the min-max principle. Asymptotically sharp bounds then follow from bounds
for Riesz-means of Laplacian eigenvalues.
