  In this paper, the main aim is to discuss the existence of the extreme points
and support points of families of harmonic Bloch mappings and little harmonic
Bloch mappings. First, in terms of the Bloch unit-valued set, we prove a
necessary condition for a harmonic Bloch mapping (resp. a little harmonic Bloch
mapping) to be an extreme point of the unit ball of the normalized harmonic
Bloch spaces (resp. the normalized little harmonic Bloch spaces) in the unit
disk $\mathbb{D}$. Then we show that a harmonic Bloch mapping $f$ is a support
point of the unit ball of the normalized harmonic Bloch spaces in $\mathbb{D}$
if and only if the Bloch unit-valued set of $f$ is not empty. We also give a
characterization for the support points of the unit ball of the harmonic Bloch
spaces in $\mathbb{D}$.
