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Portable devices like smartphones, tablets, wearable electronic devices, medical implants, wireless sensor nodes, and Internet-of-Things (IoT) devices have tremendous constraints on their energy consumption. Adding more functionalities onto the portable devices increases its energy consumption significantly. However, the energy capacity of the battery does not increase proportionally. Hence, to overcome the constraints on energy consumption, two main approaches are being undertaken by the designers to integrate more functionalities onto the energy-constrained systems. One approach involves reducing the inherent energy consumption of circuits, and the other involves harvesting energy from the ambient sources and utilizing it to power the circuits. In this thesis, both the approaches mentioned above are followed in developing energy-saving techniques for energy-constrained CMOS circuits and systems. Switched-capacitor-assisted power gating technique is proposed to reduce the leakage current of large digital circuits. Benefits in overall energy saving using nano-electromechanical switches (NEMS) for power gating is quantified on a system-on chip for a mobile platform made using a 14 nm gate length FinFET. For reducing the quiescent current in the analog front-end circuits, this thesis proposes a novel technique of realizing discrete-time (D-T) signal amplification using nano-electromechanical switches (NEMS). Apart from the three energy reduction techniques mentioned above, harvesting energy from mechanical vibrations using an efficient technique of power extraction from the piezoelectric transducer is proposed.