Information retrieval researchers develop algorithmic solutions to hard problems and insist on a proper, multifaceted evaluation of ideas. As we move towards even more complex deep learning models in a wide range of applications, questions on efficiency once again resurface with renewed urgency. Efficiency is no longer limited to time and space but has found new, challenging dimensions that stretch to resource-, sample- and 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 retrieval. It is inspired by the parallels that exist between the challenges in neural network-based ranking solutions and their predecessors, decision forest-based learning-to-rank models, and the connections between the solutions the literature to date has to offer. By understanding the fundamentals underpinning these algorithmic and data structure solutions one can better identify future directions and more efficiently determine the merits of ideas.