This paper proposes a covariant generalization of the holographic entanglement entropy proposal in the context of quantum field theories (QFTs). The goal is to understand the time-dependent behavior of entanglement entropy in generic QFTs. The authors suggest a covariant formulation of the holographic entanglement entropy, motivated by the covariant entropy bound underlying the holographic principle. They argue that the entanglement entropy associated with a region on the boundary of an AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. The construction is demonstrated with examples, showing its reduction to the standard holographic entanglement entropy in static spacetimes. The proposal is also used to understand the time evolution of entanglement entropy in a time-varying QFT state dual to a collapsing black hole background. The authors further argue that Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary. The paper discusses various constructions, including light-sheets, extremal surfaces, and other covariant methods, and examines their relations and consistency in different spacetime backgrounds. The authors also provide a detailed analysis of the entanglement entropy in time-dependent backgrounds, including examples such as Vaidya-AdS spacetimes and AdS wormholes. The paper concludes with a discussion of the implications of the covariant holographic entanglement entropy proposal for understanding the behavior of entanglement entropy in time-dependent QFTs.This paper proposes a covariant generalization of the holographic entanglement entropy proposal in the context of quantum field theories (QFTs). The goal is to understand the time-dependent behavior of entanglement entropy in generic QFTs. The authors suggest a covariant formulation of the holographic entanglement entropy, motivated by the covariant entropy bound underlying the holographic principle. They argue that the entanglement entropy associated with a region on the boundary of an AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. The construction is demonstrated with examples, showing its reduction to the standard holographic entanglement entropy in static spacetimes. The proposal is also used to understand the time evolution of entanglement entropy in a time-varying QFT state dual to a collapsing black hole background. The authors further argue that Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary. The paper discusses various constructions, including light-sheets, extremal surfaces, and other covariant methods, and examines their relations and consistency in different spacetime backgrounds. The authors also provide a detailed analysis of the entanglement entropy in time-dependent backgrounds, including examples such as Vaidya-AdS spacetimes and AdS wormholes. The paper concludes with a discussion of the implications of the covariant holographic entanglement entropy proposal for understanding the behavior of entanglement entropy in time-dependent QFTs.