Paleoclimate is the climate in the geologic past. Paleoclimatic information comes from natural archives (e.g., speleothems, marine sediment cores) and measurements of indicator or proxy variables (e.g., oxygen isotopes), while the time information comes from dated samples of the archive. Since climate archives exhibit growth changes over time, the resulting time series is unevenly spaced. Since the dating exhibits measurement error, the resulting timescale is uncertain. In addition to these two paleoclimate-specific challenges (uneven spacing, uncertain timescale), two challenges more common to statistical science appear (non-normal distributional shape, autocorrelation). We have previously shown [Mudelsee 2010, Climate Time Series Analysis, Springer; www.manfredmudelsee.com/book <http://www.manfredmudelsee.com/book>] that the bootstrap resampling approach is able to meet these four challenges. This talk illustrates various ingredients of the bootstrap adaption to paleoclimate time series analysis, namely the AR(1) process for uneven spacing, (pairwise) moving-block resampling, parametric timescale simulations, confidence interval construction and Monte Carlo tests. We exemplify our bootstrap adaptation on two estimation problems. The first is spectrum estimation and the search for solar cycles in proxy records of the Indian summer monsoon covering the past 10000 years. The second example comes from the GATEWAYS project (Multi-level assessment of ocean-climate dynamics: A gateway to interdisciplinary training and analysis) and deals with correlation estimation on paleoceanographic time series from the Agulhas region,south of South Africa. Supporting grants: This work is supported by the European Commission via the Marie Curie Initial Training Network GATEWAYS (project number 238512) under the Seventh Framework Programme. Key words: Bootstrap, Climate, Correlation, Spectrum, Time Series