As information retrieval researchers, we not only develop algorithmic solutions to hard problems, but we also insist on a proper, multifaceted evaluation of ideas. The literature on the fundamental topic of retrieval and ranking, for instance, has a rich history of studying the effectiveness of indexes, retrieval algorithms, and complex machine learning rankers, while at the same time quantifying their computational costs, from creation and training to application and inference. This is evidenced, for example, by more than a decade of research on efficient training and inference of large decision forest models in Learning to Rank (LtR). As we move towards even more complex, deep learning models in a wide range of applications, questions on efficiency have once again resurfaced with renewed urgency. Indeed, efficiency is no longer limited to time and space; instead it has found new, challenging dimensions that stretch to resource-, sampleand energy-efficiency with ramifications for researchers, users, and the environment.This monograph takes a step towards promoting the study of efficiency in the era of neural information retrieval by offering a comprehensive survey of the literature on efficiency and effectiveness in ranking, and to a limited extent, retrieval. This monograph was inspired by the parallels that exist between the challenges in neural network-based ranking solutions and their predecessors, decision forest-based LtR models, as well as the connections between the solutions the literature to date has to offer. We believe that by understanding the fundamentals underpinning these algorithmic and data structure solutions for containing the contentious relationship between efficiency and effectiveness, one can better identify future directions and more efficiently determine the merits of ideas. We also present what we believe to be important research directions in the forefront of efficiency and effectiveness in retrieval and ranking.