  We identify cluster algebras for planar kinematics of conformal Feynman
integrals in four dimensions, as sub-algebras of that for top-dimensional
$G(4,n)$ corresponding to $n$-point massless kinematics. We provide evidence
that they encode information about singularities of such Feynman integrals,
including all-loop ladders with symbol letters given by cluster variables and
algebraic generalizations. As a highly-nontrivial example, we apply $D_3$
cluster algebra to a $n=8$ three-loop wheel integral, which contains a new
square root. Based on the $D_3$ alphabet and three new algebraic letters
essentially dictated by the cluster algebra, we bootstrap its symbol, which is
strongly constrained by the cluster adjacency. By sending a point to infinity,
our results have implications for non-conformal Feynman integrals, e.g., up to
two loops the alphabet of two-mass-easy kinematics is given by limit of this
generalized $D_3$ alphabet. We also find that the reduction to three dimensions
is achieved by folding and the resulting cluster algebras may encode
singularities of amplitudes and Feynman integrals in ABJM theory, at least
through $n=7$ and two loops.
