Okay, let's take them one at a time as they present different types of problems.Loosely speaking, the bootstrap works because each resample is equally likely as the original sample. To take the discrete case, suppose I offer you a bet. We will take two observations from an unknown i.i.d. distribution, x and y. We will then continue sampling from that distribution until one of the four pairs, x,x; x,y; y,x; or y,y appears. There is one chance in four of any of those winning.Now, clearly this is not true for autocorrelated data. x,y will be more likely than the other three.One solution is to transform the data to remove the autocorrelation. Differencing will sometimes do that. In general, you could fit a time series model to the data, ARIMA or GARCH for example, then bootstrap the residuals. That goes against the non-parametric spirit of the bootstrap and introduces some theoretical difficulties (even if your model is perfect and the true residuals are i.i.d., the fitted residuals will not be). But it can give reasonable results.Another approach is to use subsamples as ClosetChartist suggested. Suppose you have N points. The simplest subsample technique is to compute your statistic on the k subsamples of length N - k + 1 for some k (k=30 might be a good choice for a well-behaved statistic), the first starting with the first point, the second starting with the second point and so on up to the kth starting at the kth point; each subsample just running forward from the starting point. You then have to adjust your distribution for the larger sample size (N, instead of N - k + 1). You can do that either by assumption (multiply by [(N - k + 1)/N]^0.5 for standard deviation for example) or by using different k's and extrapolating.Or you can ignore the autocorrelation. If your statistic does not depend on the short-term order of the points, and the series is stationary, that can work pretty well. Or not.The problem with multivariate samples with internal correlation is different. For example, suppose we have N draws of x and e, each from its own i.i.d. distribution, but the data is reported to us only as x,y with y = b*x + e and we don't know b. x and y will be correlated. The bootstrap resamples will still be equally likely in the sense above, but many of the statistics we want to compute will not bootstrap well. This is increasingly true as the dimensionality increases.An example of a statistic that bootstraps badly is the number of repeated data points in the sample. For a continuous distribution, this statistic is zero with probability one. But all the resamples except the original sample have non-zero values for it. Many statistics on high-dimensional data do not bootstrap well, although the reason is less obvious.One solution is to reduce the dimensionality, say by principal components or by fitting a model. This has the disadvantages above, although it can work. Subsampling will not help. If you can assume that your variables are all the same in some sense, say a vector of returns on different stocks for the same time period, you can compute a cross-sectional statistic first, then bootstrap in one dimension.