This thesis revolves about the relationship between orbital forcing and climate variability.  To place paleo and modern climate variability in context, the spectrum of temperature variability is estimated from time-scales of months to hundreds of thousands of years, using a patchwork of proxy and instrumental records.  There is an energetic background continuum and rich spatial structure associated with temperature variability which both scale according to simple spectral power-laws.  To complement the spatial and temporal analysis of temperature variability, a description of the full insolation forcing is also developed using Legendre polynomials to represent the spatial modes of variability, and singular vectors to represent seasonal and long-term changes.  The leading four spatial and temporal modes describe over 99% of the insolation variability, making this a relatively simple and compact description of the full insolation forcing.  Particular attention is paid to the insolation variations resulting from the precession of the equinoxes.  There is no mean annual insolation variability associated with precession--precession only modulates the seasonal cycle.  Nonlinear rectification of the seasonal cycle generates precession-period variability, and such reactivation naturally occurs in the climate system but also results from the seasonality inherent to many climate proxies.  One must distinguish this latter instrumental effect from true climate responses.  Another potential source of spurious low-frequency variability results from the stretching and squeezing of an age-model, so that noise in a record is made to align with an orbital signal.  Furthermore, and contrary to assertions made elsewhere, such orbital-tuning can also generate an eccentricity-like amplitude modulation in records that have been narrow-band-pass filtered over the precession bands.

An accurate age-model is the linchpin required to connect insolation forcing with any resulting climatic responses; to avoid circular reasoning, this age-model should make no orbital assumptions.  A new chronology of glaciation, spanning the last 780 kilo-years is estimated from 21 marine sediment cores, using a compaction-corrected depth scale as a proxy for time.  Age-model uncertainty estimates are made using a stochastic model of marine sediment accumulation.  The depth-derived ages are estimated to be accurate to within +/-9000 years, and within this uncertainty are consistent with the orbitally-tuned age estimates.  Nonetheless, the remaining differences between the depth and orbitally derived chronologies produce important differences in the spectral domain.  From the delta-18O record, using the depth-derived ages, evidence is found for a nonlinear coupling involving the 100KY and obliquity frequency bands which generates interaction bands at sum and difference frequencies.  If an orbitally-tuned age-model is instead applied, these interactions are suppressed, with the system appearing more nearly linear.

A generalized phase synchronization analysis is used to further assess the nonlinear coupling between obliquity and the glacial cycles.  Using a formal hypothesis testing procedure, it is shown that glacial terminations are associated with high-obliquity states at the 95% significance level.  The association of terminations with eccentricity or precession is indistinguishable from chance.  A simple excitable system is introduced to explore potential mechanisms by which obliquity paces the glacial cycles.  After tuning a small number of adjustable parameters, the excitable model reproduces the correct timing for each termination as well as the linear and nonlinear features earlier identified in the delta-18O record. Under a wide range of conditions, the model exhibits a chaotic amplitude response to insolation forcing.  One chaotic mode gives a train of small and nearly equal amplitude 40KY cycles.  Another mode permits ice to accumulate over two (80KY) or three obliquity cycles (120KY) prior to rapidly ablating and thus, on average, generates 100KY variability.  The model spontaneously switches between these 40 and 100KY chaotic modes, suggesting that the Mid-Pleistocene Transition may be independent of any major shifts in the background state of the climate system.