  In this paper we report on recent results by several authors, on the spectral
theory of lens spaces and orbifolds and similar locally symmetric spaces of
rank one. Most of these results are related to those obtained by the authors in
[IMRN (2016), 1054--1089], where the spectra of lens spaces were described in
terms of the one-norm spectrum of a naturally associated congruence lattice. As
a consequence, the first examples of Riemannian manifolds isospectral on
$p$-forms for all $p$ but not strongly isospectral were constructed.
  We also give a new elementary proof in the case of the spectrum on functions.
In this proof, representation theory of compact Lie groups is avoided and
replaced by the use of Molien's formula and a manipulation of the one-norm
generating function associated to a congruence lattice. In the last four
sections we present several recent results, open problems and conjectures on
the subject.
