  This article surveys the analytic aspects of the author's recent studies on
the construction and analysis of a "geometrically canonical" Laplacian on
circle packing fractals invariant with respect to certain Kleinian groups
(i.e., discrete groups of M\"{o}bius transformations on the Riemann sphere
$\widehat{\mathbb{C}}=\mathbb{C}\cup\{\infty\}$), including the classical
Apollonian gasket and some round Sierpi\'{n}ski carpets. The main result on
Weyl's asymptotics for its eigenvalues is of the same form as that by Oh and
Shah [Invent. Math. 187 (2012), 1--35, Theorem 1.4] on the asymptotic
distribution of the circles in a very large class of such fractals.
