The evolution of wireless communication toward next-generation networks introduces unprecedented demands on data rates, latency, and connectivity. To meet these requirements, two key trends have emerged: the use of higher communication frequencies to provide broader bandwidth, and the deployment of massive multiple-input multiple-output systems with large antenna arrays to compensate for propagation losses and enhance spatial multiplexing. These advancements significantly extend the Rayleigh distance, enabling near-field (NF) propagation alongside the traditional far-field (FF) regime. As user communication distances dynamically span both FF and NF regions, cross-field (CF) communication has also emerged as a practical consideration. Beam management (BM)-including beam scanning, channel state information estimation, beamforming, and beam tracking-plays a central role in maintaining reliable directional communications. While most existing BM techniques are developed for FF channels, recent works begin to address the unique characteristics of NF and CF regimes. This survey presents a comprehensive review of BM techniques from the perspective of propagation fields. We begin by building the basic through analyzing the modeling of FF, NF, and CF channels, along with the associated beam patterns for alignment. Then, we categorize BM techniques by methodologies, and discuss their operational differences across propagation regimes, highlighting how field-dependent channel characteristics influence design tradeoffs and implementation complexity. In addition, for each BM method, we identify open challenges and future research directions, including extending FF methods to NF or CF scenarios, developing unified BM strategies for field-agnostic deployment, and designing low-overhead BM solutions for dynamic environments.