  In this article, the authors establish the pointwise characterization of
Besov and Triebel-Lizorkin spaces on spaces of homogeneous type via clarifying
the relationship among Haj\l asz-Sobolev spaces, Haj\l asz-Besov and Haj\l
asz-Triebel-Lizorkin spaces, grand Besov and Triebel-Lizorkin spaces, and Besov
and Triebel-Lizorkin spaces. A major novelty of this article is that all
results presented in this article get rid of both the dependence on the reverse
doubling condition of the measure and the metric condition of the quasi-metric
under consideration. Moreover, the pointwise characterization of the
inhomogeneous version is new even when the underlying space is an RD-space.
