The traditional uncorrelated least squares fit can be generalized to the situation with data correlation (e.g. caused by data filtering which is essential to minimize noise), which has been applied to cavity ring-down spectroscopy (CRDS). The ideal accuracy limit of the extracted decay rate k was derived from the exponential decay signal for both white noise dominated and shot noise dominated CRDS. Different algorithms of single exponential fitting in CRDS were reviewed by comparing the bias and variance estimation of the extracted k, and computation efficiency of different fitting methods. In continuous wave (CW) CRDS, it was found that the very high order (∼ 60th) transverse mode can be excited simultaneously with the TEM00 mode through mirror surface scattering coupling when they are near degenerate. This will lead to mode beating noise in ring-down transients even when the intensity coupling strength is extremely small, ∼ 10-12 per reflection. Putting an intracavity aperture of the right size will remove this noise by suppressing the excitation of high order transverse modes. Linear residual or strain induced birefringence (10-7 ∼ 10-6 rad) in high reflective (HR) coatings of supermirrors will lift the degeneracy of TEM00 mode between two polarizations, generating two new eigen polarization states, which are very close to linear polarization and have a typical splitting of 0.1 kHz. Because of the polarization dependent loss (linear dichroism, ∼ 10-8) of HR coatings of supermirrors, these two new eigenstates are no longer orthogonal with each other, producing mode beating noise in ring-down signal. By controlling the polarization state of the incident light or in the detection, this noise can be removed. Because of finite extinction ratio of the light modulator in CW-CRDS, the small light leakage will interfere with the exponential decay of intracavity light power, generating excess noise in the signal. A linear relation between (sigmak/k)2 and the extinction ratio has been found both theoretically and experimentally, with excellent agreement. In order to realize the ideal sensitivity (See Chapter 2) in CW-CRDS, light modulator with very high extinction ratio is needed. The efficacy of using a semiconductor optical amplifier (SOA) as light modulator in CW-CRDS was demonstrated. SOA has the highest extinction ratio (>80 dB). For ring-down transients with S/N of 1400:1, the SOA and acousto-optic modulator (AOM) are found to give equivalent performance. The Allan variance was applied to characterize the drifting of the decay rate in CW-CRDS experiments. With differential measurements by two lasers between k and k0, the decay rates with and without absorption, the drifting between them will cancel out with each other greatly. A sensitivity of 5.6 x 10-12 cm -1 has been reached within an integration time of 15.4 minutes, which corresponds to trace methane detection limit (3sigma) of 0.3 parts per billion by volume (ppbv) at 20 torr or 15 parts per trillion by volume (pptv) at one atm measurement pressure around 1652 nm. By converting CO, CO2, ethane, propane and n-butane into methane with 100% conversion efficiency under the condition of excess H2 gas and nickel (or ruthenium) catalyst (for isobutane, the conversion efficiency is about 80%), each trace gas has been measured in nitrogen separately down to the level of sub parts per million by volume (ppmv), limited by ∼ 0.5 ppmv methane background in the conversion caused by the carbon contamination of both catalysts.