This work provides an analysis of checkpointing strategies for minimizing expected job execution times in an environ- ment that is subject to processor failures. In the case of both sequential and parallel jobs, we give the optimal solu- tion for exponentially distributed failure inter-arrival times, which, to the best of our knowledge, is the first rigorous proof that periodic checkpointing is optimal. For non-ex- ponentially distributed failures, we develop a dynamic pro- gramming algorithm to maximize the amount of work com- pleted before the next failure, which provides a good heuris- tic for minimizing the expected execution time. Our work considers various models of job parallelism and of parallel checkpointing overhead. We first perform extensive simula- tion experiments assuming that failures follow Exponential or Weibull distributions, the latter being more representa- tive of real-world systems. The obtained results not only corroborate our theoretical findings, but also show that our dynamic programming algorithm significantly outperforms previously proposed solutions in the case of Weibull fail- ures. We then discuss results from simulation experiments that use failure logs from production clusters. These results confirm that our dynamic programming algorithm signifi- cantly outperforms existing solutions for real-world clusters.