This paper explores the properties and implications of $q$-form global symmetries, where charged operators are of space-time dimension $q$ and charged excitations have $q$ spatial dimensions. These symmetries, which include Wilson lines, surface defects, strings, and membranes, share many properties with ordinary global symmetries ($q = 0$), such as Ward identities and selection rules on amplitudes. They can be coupled to classical background fields and gauged by summing over these fields. These generalized global symmetries can be spontaneously broken and may have 't Hooft anomalies, which prevent gauging but lead to anomaly matching conditions. The paper discusses the classification of phases of 4d gauge theories using spontaneous breaking of one-form global symmetries and the role of anomalies in boundary effects and long-range order on domain walls. It also presents examples of theories and their higher-form global symmetries, including a $U(1)$ gauge theory in 4d and a non-Abelian gauge theory in 4d. The authors provide a unified perspective on various known phenomena and uncover new results.This paper explores the properties and implications of $q$-form global symmetries, where charged operators are of space-time dimension $q$ and charged excitations have $q$ spatial dimensions. These symmetries, which include Wilson lines, surface defects, strings, and membranes, share many properties with ordinary global symmetries ($q = 0$), such as Ward identities and selection rules on amplitudes. They can be coupled to classical background fields and gauged by summing over these fields. These generalized global symmetries can be spontaneously broken and may have 't Hooft anomalies, which prevent gauging but lead to anomaly matching conditions. The paper discusses the classification of phases of 4d gauge theories using spontaneous breaking of one-form global symmetries and the role of anomalies in boundary effects and long-range order on domain walls. It also presents examples of theories and their higher-form global symmetries, including a $U(1)$ gauge theory in 4d and a non-Abelian gauge theory in 4d. The authors provide a unified perspective on various known phenomena and uncover new results.