For close to a century, researchers from across the disciplines of Urban Studies have developed empirical models for understanding the spatial extent and social composition of urban neighborhoods--and how these dimensions change over time. Unfortunately, however, these techniques have often been developed within disciplinary silos and without broad exposure to other potentially interested constituencies. In this paper, we traverse the literatures of social science, computer science, and statistics to examine a variety of modeling techniques for understanding neighborhood dynamics. We begin our review by examining early concepts of spatial structure first outlined in the Chicago School and discuss how the notions of social ecology and quantitative neighborhood analysis permeated the urban studies for several decades to come. Our survey continues by reviewing contemporary statistical approaches for identifying urban neighborhoods, culminating with the state of the art in subfields known as `geodemographics' and `regionalization'. Following this review, we offer insight into the field's persistent conceptual issues, identify areas ripe for additional research, and highlight newly-developed computational methods that can inform more just and socially equitable public policy, community development, and accountable governance.