This review provides an introductory guide to the central concepts and challenges in superconducting quantum circuits, focusing on quantum engineering. It covers qubit design, noise properties, qubit control, and readout techniques, bridging fundamental concepts in circuit quantum electrodynamics (cQED) with contemporary applications in gate-model quantum computation. The article is organized into sections discussing quantum circuits, noise, error mitigation, qubit control, and readout methods. Section II explores the parameter space available in superconducting circuits, focusing on capacitively-shunted planar qubit modalities and their engineering. It discusses how qubit transition frequency, anharmonicity, and noise susceptibility can be tailored through circuit topology and element parameters. The section also introduces methods for engineering interactions between qubits to implement two-qubit entangling operations. Section III discusses systematic and stochastic noise, noise strength, and qubit noise susceptibility. It introduces the Bloch-Redfield model of decoherence, characterized by longitudinal and transverse relaxation times $ T_1 $ and $ T_2 $, and discusses the implications of 1/f noise. The noise power spectral density is defined and its role in driving decoherence is described. The section also reviews coherent control methods used to mitigate coherence and reversible noise. Section IV provides a review of how single- and two-qubit operations are implemented in superconducting circuits using local magnetic flux control and microwave drives. It discusses the family of two-qubit gates arising from capacitive coupling between qubits and recent advances in achieving high-fidelity gates. The continued development of high-fidelity two-qubit gates is a highly active research area, and the review includes sufficient technical details for readers to critically assess various gates. Section V discusses the physics and engineering associated with dispersive readout, typically used to measure qubit states. It covers the theory behind dispersive coupling, the design of Purcell filters, and the development of quantum-limited parametric amplifiers. The article also discusses the transmon qubit, a key component in superconducting quantum circuits, and its evolution into tunable qubits with split transmon designs. It explores the introduction of nonlinearity through Josephson junctions to achieve anharmonicity, leading to the flux qubit and fluxonium qubit. These qubits offer greater anharmonicity and improved coherence times. The review also discusses interaction Hamiltonian engineering, focusing on capacitive and inductive coupling mechanisms. It explains how these couplings are represented in the qubit eigenbasis and how they enable the implementation of two-qubit gates. The coupling axis is discussed in terms of transverse and longitudinal coupling, with transverse coupling involving off-diagonal matrix elements and longitudinal coupling involving diagonal elements. The article concludes with a summary and outlook, emphasizing the importance of quantum engineering in advancing superconducting quantum computing. It highlights the need for continued research and development in this field to achieve scalable and fault-tolerantThis review provides an introductory guide to the central concepts and challenges in superconducting quantum circuits, focusing on quantum engineering. It covers qubit design, noise properties, qubit control, and readout techniques, bridging fundamental concepts in circuit quantum electrodynamics (cQED) with contemporary applications in gate-model quantum computation. The article is organized into sections discussing quantum circuits, noise, error mitigation, qubit control, and readout methods. Section II explores the parameter space available in superconducting circuits, focusing on capacitively-shunted planar qubit modalities and their engineering. It discusses how qubit transition frequency, anharmonicity, and noise susceptibility can be tailored through circuit topology and element parameters. The section also introduces methods for engineering interactions between qubits to implement two-qubit entangling operations. Section III discusses systematic and stochastic noise, noise strength, and qubit noise susceptibility. It introduces the Bloch-Redfield model of decoherence, characterized by longitudinal and transverse relaxation times $ T_1 $ and $ T_2 $, and discusses the implications of 1/f noise. The noise power spectral density is defined and its role in driving decoherence is described. The section also reviews coherent control methods used to mitigate coherence and reversible noise. Section IV provides a review of how single- and two-qubit operations are implemented in superconducting circuits using local magnetic flux control and microwave drives. It discusses the family of two-qubit gates arising from capacitive coupling between qubits and recent advances in achieving high-fidelity gates. The continued development of high-fidelity two-qubit gates is a highly active research area, and the review includes sufficient technical details for readers to critically assess various gates. Section V discusses the physics and engineering associated with dispersive readout, typically used to measure qubit states. It covers the theory behind dispersive coupling, the design of Purcell filters, and the development of quantum-limited parametric amplifiers. The article also discusses the transmon qubit, a key component in superconducting quantum circuits, and its evolution into tunable qubits with split transmon designs. It explores the introduction of nonlinearity through Josephson junctions to achieve anharmonicity, leading to the flux qubit and fluxonium qubit. These qubits offer greater anharmonicity and improved coherence times. The review also discusses interaction Hamiltonian engineering, focusing on capacitive and inductive coupling mechanisms. It explains how these couplings are represented in the qubit eigenbasis and how they enable the implementation of two-qubit gates. The coupling axis is discussed in terms of transverse and longitudinal coupling, with transverse coupling involving off-diagonal matrix elements and longitudinal coupling involving diagonal elements. The article concludes with a summary and outlook, emphasizing the importance of quantum engineering in advancing superconducting quantum computing. It highlights the need for continued research and development in this field to achieve scalable and fault-tolerant