Tropical Andean glaciers are an essential component of the alpine Earth System providing vital water resources for life in their vicinity. Glaciers are also archives of past climate change and barometers of present climate change, and tropical glaciers can provide a much-needed additional low-latitude terrestrial paleoclimate proxy. Despite their societal and scientific importance, the study of tropical glaciers is nascent. This dissertation provides new perspectives on the climate components most important for tropical glacier change, illustrates that records of past tropical glacier changes can be used as a quantitive paleoclimate proxy, and provides a framework for a more rigorous interpretation of tropical glacier advances and retreats as a climate proxy. A regional-scale surface energy and mass balance model is developed and implemented to quantify tropical glacier response to different types of climate change. The mass balance evolution from thermal year (July - June) 1980 - 2009 CE is simulated, and the dominant input climate variables are determined. The dominant climate drivers of glacier change at tropical Andean glaciers vary, depending on the regional climate setting and in particular the amount of annual precipitation. For both wet inner tropical glaciers and wet outer tropical glaciers, interannual temperature variability is the dominant climate forcing mechanism for equilibrium line altitude (ELA) or mass balance variability. For dry tropical glaciers, precipitation variability is the dominant variable for mass balance and ELA variability. For tropical glaciers, all-wave radiation (i.e. net shortwave and longwave radiation) is the dominant source of available melt energy, and at wet tropical glaciers, which is the classification type of the majority of Andean glaciers, temperature is able to modulate the all-wave radiation from year-to-year. By dictating the phase of precipitation temperature determines the surface albedo and absorbed shortwave radiation at the lowest extents of the glacier, and this relationship is so strong that it can define the glacier-wide mass balance. Thus, for wet tropical glaciers, observations of mass balance or length changes primarily reflects temperature change. A coupled ice flow and surface mass balance model is implemented at the world's largest tropical ice mass, the Quelccaya Ice Cap, Peru, to invert the Little Ice Age and Younger Dryas aged moraines into quantitive paleoclimate proxies. Temperature is shown to be the dominant climate driver for changes in extent for the Huancane Valley outlet glacier. Temperature coolings at the ice cap of between 0.7 deg. C and 1.1 deg. C could advance the glacier to the position of the Little Ice Age moraines. Temperature coolings at the ice cap of between 0.9 deg. C and 2.6 deg. C could advance the glacier to the position of the Younger Dryas moraines. These ice cap coolings are extrapolated along the moist adiabat curve to sea surface temperature (SST) coolings and correspond to tropical SST coolings of between 0.4 deg. C and 0.6 deg. C during the Little Ice Age and between 0.5 deg. C and 1.5 deg. C for the Younger Dryas. These coolings are compared to tropical SST coolings realized in paleoclimate general climate model simulations. They agree well with simulations that include climate forcing mechanisms thought to be important during each respective centennial/millennial-scale climate change event. An ice flow model and idealized representation of how glacier mass balance responds to interannual climate variability are implemented to determine the long-term impact of interannual climate variability on the long-term glacier mass balance and length. Changes in the magnitude of temperature variability drive changes in the net mass balance and the mean glacier length, due to a mass balance asymmetry between anomalously warm years and anomalously cold years. A warm year ablates more anomalous mass than can be compensated by anomalous accumulation on an similarly cold year, producing a mass balance nonlinearity. The nonlinearity stems from a nonlinear vertical mass balance profile, with steeper mass balance gradients in the ablation zone than the accumulation zone. The size of the nonlinearity reflects the difference in mass balance gradients between the accumulation and ablation zones as well as the size of the temperature variability. For the same magnitude of temperature variability, glaciers with very steep ablation zone mass balance gradients and shallow accumulation zone mass balance gradients, such as tropical glaciers, will experience larger mass balance nonlinearities as compared to glaciers with a smaller difference between their mass balance gradients, such as mid latitude glaciers. Since the mass balance nonlinearity stemming from interannual temperature variability is greater for tropical glaciers, consideration of length changes due to changes in the statistics of interannual temperature variability should be taken into account for tropical glaciers when interpreting the climate signal embedded in length changes. The key findings of this dissertation indicate that the vast majority of tropical Andean glaciers are highly sensitive to temperature change and variability. These highly sensitive glaciers are wet tropical glaciers in regions that receive at least 0.75 meters water equivalent per year of precipitation. This strong linkage between temperature and mass balance or length changes indicates that tropical glaciers can make for good paleo-thermometers and that their longterm evolution will primarily reflect temperature changes. A portion of past length changes and future length changes may also reflect changes in the amount of interannual temperature variability, which stems from a universal mass balance nonlinearity which is especially acute for tropical glaciers. In closing, the strong relationship between temperature and glacier variability for the vast majority of the world's tropical glaciers highlights their continued and perhaps accelerated disappearance in an anthropogenic warming world.