Recent experiments with hundreds to thousands of Rydberg atoms arranged in two-dimensional arrays have shown remarkable progress in analog quantum simulation and computation. Extending these atomic arrays to three dimensions is expected to enable richer qubit connectivity and the implementation of various Hamiltonians. In this talk, we present our work on the application of three-dimensional Rydberg atom arrays for quantum simulation and computation. As a relevant experiment, we have observed the quantum dynamics of Rydberg atom clusters with up to  N=13. From these dynamics, we discuss antiferromagnetic spin correlations between interlayer Rydberg atoms and their applicability to maximum independent set problems involving non-planar graphs. Furthermore, we address computational complexity in adiabatic quantum computation based on unit-ball and k-PXP graphs, together with current experimental progress toward this goal.