Cartograms are value-by-area maps which modify geographic regions, such as countries, in proportion to some variable of interest, such as population. These are popular georeferenced data visualizations that have been used for over a century to illustrate patterns and trends in the world around us. A wide variety of cartogram types exist, that were designed to optimize different cartogram dimensions, such as geographic accuracy and statistical accuracy. This work surveys cartogram research in visualization, cartography and geometry, covering a broad spectrum of different cartogram types: from the traditional rectangular cartograms, to Dorling and diffusion cartograms. Based on prior work in visualization and cartography, I propose a task taxonomy of cartograms, and describe a study of cartograms based on quantitative metric-based comparisons, task-based time-and-error evaluation, and subjective preference and feedback analysis. For these evaluations, I considered four major types of cartograms which allowed us to compare and analyze the evaluation strategies and discuss the implications of the surprising outcomes. In the context of maps, the ability to recall information shown in the map is one of the important factors in determining effectiveness. In spite of some early studies that involved cartograms, the memorability of different cartogram types has not been investigated. In order to create effective data presentations, we first need to understand what makes a visualization memorable. I investigate the memorability of contiguous and Dorling cartograms, both in terms of recognition of the map and recall of data. Finally, I describe bivariate cartograms, a technique specifically designed to allow for the simultaneous comparison of two geo-statistical variables. Traditional cartograms are designed to show only a single statistical variable, but in practice, it is often useful to show two variables (e.g., the total sales for two competing companies) simultaneously. Bivariate cartograms make it easy to find geographic patterns and outliers in a pre-attentive way. They are most effective for showing two variables from the same domain (e.g., population in two different years, sales for two different companies), although they can also be used for variables from different domains (e.g., population and income). I also describe a small-scale evaluation of the proposed techniques that indicates bivariate cartograms are especially effective for finding geo-statistical patterns, trends and outliers.