A block map is a map
f
:
{
0
,
1
}
n
→
{
0
,
1
}
f:\,{\{ {\text {0}},\,{\text {1}}\} ^n}\, \to \,\{ 0,\,1\}
for some
n
⩾
1
n\, \geqslant \,1
. A block map f induces an endomorphism
f
∞
{f_\infty }
of the full 2-shift
(
X
,
σ
)
(X,\,\sigma )
. We define composition of block maps so that
(
f
∘
g
)
∞
=
f
∞
∘
g
∞
{(f \circ g)_\infty }\, = \,{f_\infty } \circ {g_\infty }
. The commuting block maps problem (for f) is to determine
C
(
f
)
=
{
g
|
f
∘
g
=
g
∘
f
}
\mathcal {C}(f)\, = \,\{ g|f \circ g\, = \,g \circ f\}
. We solve the commuting block maps problem for a number of classes of block maps.