This thesis first reviews existing work in CMOS active inductors focusing on two implementations, Wu gyrator-C and differential floating active inductors. It then proposes a new method of quantifying the performance of active inductors by introducing a figure of merit called "mean quality factor" that is better suited to the large signal behavior of active inductors. New CMOS constant-Q active inductors are proposed that are intended specifically for applications where a large signal operation in required. The thesis then proposes CMOS active transformers that are active circuit equivalents of two magnetically coupled coils. Four applications of constant-Q active inductors and active transformers namely a 2.4 GHz voltage-controlled oscillator with -119.5dBc/Hz phase noise at 1 MHz offset, a 2.4 GHz current-mode phase-locked loop with -116dBc/Hz phase noise at 1 MHz offset and 80ns lock time, a 5 MHz 100X oversampled current-mode sigma-delta modulator with 50dB dynamic range and 65dB SNR, and a 1.6 GHz QPSK phase modulator with -101dBc/Hz phase noise at 1 MHz offset are presented.