  Neutral atom technology has steadily demonstrated significant theoretical and
experimental advancements, positioning itself as a front-runner platform for
running quantum algorithms. One unique advantage of this technology lies in the
ability to reconfigure the geometry of the qubit register, from shot to shot.
This unique feature makes possible the native embedding of graph-structured
problems at the hardware level, with profound consequences for the resolution
of complex optimization and machine learning tasks. By driving qubits, one can
generate processed quantum states which retain graph complex properties. These
states can then be leveraged to offer direct solutions to problems or as
resources in hybrid quantum-classical schemes. In this paper, we review the
advancements in quantum algorithms for graph problems running on neutral atom
Quantum Processing Units (QPUs), and discuss recently introduced embedding and
problem-solving techniques. In addition, we clarify ongoing advancements in
hardware, with an emphasis on enhancing the scalability, controllability and
computation repetition rate of neutral atom QPUs.
