  We review recent studies of the cluster structure of light nuclei within the
framework of the algebraic cluster model (ACM) for nuclei composed of k
alpha-particles and within the framework of the cluster shell model (CSM) for
nuclei composed of k alpha-particles plus x additional nucleons. The
calculations, based on symmetry considerations and thus for the most part given
in analytic form, are compared with experiments in light cluster nuclei. The
comparison shows evidence for Z_2, D_{3h} and T_d symmetry in the even-even
nuclei 8Be (k=2), 12C (k=3) and 16O (k=4), respectively, and for the associated
double groups Z'_2 and D'_{3h} in the odd nuclei 9Be, 9B (k=2, x=1) and 13C
(k=3, x=1), respectively.
