Dynamical decoupling pulse sequences have been used to extend coherence times in quantum systems ever since the discovery of the spin-echo effect. But while for good reasons the nuclear magnetic resonance (NMR) community has typically been content with moderate line narrowing, in quantum computing extremely high levels of coherence are required in order to perform meaningful computational tasks. In this talk I will describe a method of recursively concatenated dynamical decoupling pulses, designed to overcome both decoherence and operational errors [1]. For bounded-strength, non-Markovian environments, such as for the spin-bath that arises in electron- and nuclear-spin based solid-state quantum computer proposals, it is strictly advantageous to use concatenated, as opposed to standard periodic dynamical decoupling pulse sequences. Namely, the concatenated scheme is both fault-tolerant and super-polynomially more efficient, at equal cost [2,3]. Preliminary experimental results on NMR of 13C in adamantene (due to Dieter Suter, Dortmund), and NMR of the 31P donor in Si (due to Steve Lyon, Princeton), demonstrating the advantages of concatenated decoupling, will also be presented. Time permitting, I will describe our recent results on the construction of a universal set of quantum logic gates whose fidelity can be kept arbitrarily high for essentially arbitrarily long times in the presence of coupling to a spin bath, by use of concatenated decoupling. References: [1] K. Khodjasteh and D.A. Lidar, "Fault-Tolerant Quantum Dynamical Decoupling," Phys. Rev. Lett. 95, 180501 (2005). [2] K. Khodjasteh and D.A. Lidar, "Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences," Phys. Rev. A 75, 062310 (2007). [3] K. Khodjasteh and D.A. Lidar, "Rigorous Bounds on the Performance of a Hybrid Dynamical Decoupling-Quantum Computing Scheme," Phys. Rev. A 78, 012355 (2008).