Measurement-based quantum computation (MQC) is a promising approach to quantum information processing, where quantum information is processed through adaptive measurements on a highly entangled resource state, such as the 2D-cluster state. This model, particularly the one-way quantum computer, offers a new conceptual framework for quantum computation, enabling scalable and fault-tolerant operations. The 2D-cluster state serves as a universal resource for quantum computation, with its entanglement structure determining the computational power of the system. MQC has been shown to be equivalent to the quantum circuit model in terms of computational power, but differs in practical implementation and fault tolerance. MQC has practical advantages in various physical systems, including optical lattices, where cold atoms can be used to create cluster states. However, challenges remain in addressing individual lattice sites and achieving high-efficiency single-photon detection. Hybrid optical-matter schemes, combining matter qubits with linear optics, offer promising avenues for scalable quantum computation. Topological protection of information is also a key aspect of MQC, with 3D cluster states combining universality with topological error correction capabilities. Theoretical studies have shown that fault-tolerant quantum computation is possible with certain error thresholds, and that MQC can be combined with topological error correction to achieve scalable quantum computation. The universality of MQC is closely related to the entanglement properties of the resource state, with certain states being more suitable for universal computation. Classical simulation of MQC has been studied, with some states being efficiently simulatable, while others are not. MQC also has connections to classical statistical mechanics, with the Ising model being mapped to MQC models. This connection highlights the computational power of MQC and the possibility of efficient classical simulation. The study of MQC continues to be an active area of research, with ongoing efforts to improve experimental implementations and theoretical understanding of quantum computation.Measurement-based quantum computation (MQC) is a promising approach to quantum information processing, where quantum information is processed through adaptive measurements on a highly entangled resource state, such as the 2D-cluster state. This model, particularly the one-way quantum computer, offers a new conceptual framework for quantum computation, enabling scalable and fault-tolerant operations. The 2D-cluster state serves as a universal resource for quantum computation, with its entanglement structure determining the computational power of the system. MQC has been shown to be equivalent to the quantum circuit model in terms of computational power, but differs in practical implementation and fault tolerance. MQC has practical advantages in various physical systems, including optical lattices, where cold atoms can be used to create cluster states. However, challenges remain in addressing individual lattice sites and achieving high-efficiency single-photon detection. Hybrid optical-matter schemes, combining matter qubits with linear optics, offer promising avenues for scalable quantum computation. Topological protection of information is also a key aspect of MQC, with 3D cluster states combining universality with topological error correction capabilities. Theoretical studies have shown that fault-tolerant quantum computation is possible with certain error thresholds, and that MQC can be combined with topological error correction to achieve scalable quantum computation. The universality of MQC is closely related to the entanglement properties of the resource state, with certain states being more suitable for universal computation. Classical simulation of MQC has been studied, with some states being efficiently simulatable, while others are not. MQC also has connections to classical statistical mechanics, with the Ising model being mapped to MQC models. This connection highlights the computational power of MQC and the possibility of efficient classical simulation. The study of MQC continues to be an active area of research, with ongoing efforts to improve experimental implementations and theoretical understanding of quantum computation.