A review of the principles and practical implementation of quantum processors based on solid state superconducting and semiconductor spin qubits. The focus is on hardware with no overlap with existing Quantum Information or proposed Quantum Algorithms undergraduate EngSci or CompSci courses. A top-down approach is taken starting from the quantum processor architecture and building block specification, to qubit and control and readout circuit modelling, design, fabrication and testing. Topics include the basics of quantum mechanics and quantum computing, superconducting and semiconductor spin qubit physics, fabrication and characterization techniques for qubits, and classical control and readout of qubits. Students will gain hands-on experience with the engineering of a quantum computer, deriving specifications for its quantum and classical hardware building blocks, and designing, modelling, simulating, and testing qubits, control and readout circuits for quantum processors.