  The manipulation of neutral atoms by light is at the heart of countless
scientific discoveries in the field of quantum physics in the last three
decades. The level of control that has been achieved at the single particle
level within arrays of optical traps, while preserving the fundamental
properties of quantum matter (coherence, entanglement, superposition), makes
these technologies prime candidates to implement disruptive computation
paradigms. In this paper, we review the main characteristics of these devices
from atoms / qubits to application interfaces, and propose a classification of
a wide variety of tasks that can already be addressed in a computationally
efficient manner in the Noisy Intermediate Scale Quantum era we are in. We
illustrate how applications ranging from optimization challenges to simulation
of quantum systems can be explored either at the digital level (programming
gate-based circuits) or at the analog level (programming Hamiltonian
sequences). We give evidence of the intrinsic scalability of neutral atom
quantum processors in the 100-1,000 qubits range and introduce prospects for
universal fault tolerant quantum computing and applications beyond quantum
computing.
