Quantum error correction (QEC) is believed to be essential for building large-scale quantum computers, yet turning this idea into practice poses major scientific and engineering challenges. In this talk, I will describe recent experiments with reconfigurable arrays of up to 448 neutral atoms that demonstrate all key ingredients of a universal, fault-tolerant quantum architecture. I will begin with surface-code experiments showing how repeated rounds of QEC suppress errors below threshold, aided by atom-loss detection and machine-learning decoding. I will then discuss how we create logical entanglement using transversal gates and lattice surgery, and extend this to universal logic via transversal teleportation with three-dimensional codes, enabling efficient arbitrary-angle synthesis. Finally, I will show how mid-circuit qubit re-use boosts experimental throughput by two orders of magnitude, allowing us to run deep circuits with dozens of logical qubits and hundreds of teleportations while keeping entropy under control. Together, these advances illustrate the interplay of quantum logic and entropy removal, highlight the role of teleportation and reset in achieving universality, and outline design principles for scalable fault-tolerant quantum computing with neutral-atom platforms.