In the first portion of the talk, I will discuss the use of subsampling to construct p-values for hypothesis tests. The p-values are based on a modification of the usual subsampling hypothesis tests that involves centering the subsampled test statistics as in the construction of confidence intervals. This modification makes the hypothesis tests more powerful, and as a consequence provides meaningful p-values. The new p-values are shown to be asymptotically uniform under the null hypothesis and to converge zero under the alternative. \\ The second half of the talk addresses the problem of estimating the autocovariance matrix of a stationary process. The proposed estimator is a gradually tapered version of the sample autocovariance matrix in which the main diagonals are fully weighted, and the off-diagonal entries are tapered towards zero. Under short range introduce a new resampling scheme for stationary processes, which we call the Linear Process Bootstrap (LPB). The LPB is asymptotically valid for the sample mean and related statistics, and conjectured to be valid for all statistics which depend only on the first two moments of the data.