Semiconductor lasers subject to optical feedback exhibit a wide range of nonlinear dynamics such as stable emission, regular pulsing, switching, and chaos. The chaotic dynamics gives interesting random-like broadband intensity waveforms for high-speed random number generation, secure communications, and ranging. The switching dynamics that generates periodic optical waveforms has also raised interest in signal processing and communications. Common to these dynamics is a role of the delay time of the feedback, which corresponds to an undesirable time-delay signature (TDS) in chaotic signals or a useful switching period in square wave (SW) signals. As a residual peak in the intensity autocorrelation function (ACF), the TDS is detrimental to the security in chaos communications and the quality in random bit generation (RBG). In this thesis, the time-delay characteristics of semiconductor lasers subject to optical feedback are investigated. The main focus is on the generation of chaotic dynamics with TDS suppression. Firstly, TDS suppression is experimentally demonstrated by introducing a fiber Bragg grating (FBG) in place of a mirror for providing distributed feedback. The TDS is typically suppressed by over an order of magnitude to about 0.04 with a large chaotic bandwidth (CBW) of around 10 GHz. The TDS is sensitive to the detuning between the Bragg frequency and the free-running laser frequency. Best suppression is attained near the spectral edge of the FBG with a positive detuning due to chromatic dispersion and the antiguidance effect. The results enable high-speed RBG with a continuously tunable output rate. Secondly, TDS suppression by dispersive feedback using an all-pass filter (APF) is developed. Realized by coupling the feedback path to a lossless ring cavity, the APF provides dispersion to suppress the TDS while maintaining a large CBW. Thirdly, TDS suppression is numerically investigated through nonlinear fiber propagation of optical chaos with self-phase modulation (SPM). Chaotic TDS suppression and bandwidth enhancement are simultaneously attained by pulse compression and splitting. Additionally, the thesis investigates the SW switching dynamics using a semiconductor ring laser (SRL) under optical feedback. SRLs exhibit unique dynamics as they support longitudinal modes in both counter-clockwise (CCW) and clockwise (CW) directions. Compared to a Fabry-Perot laser (FPL), the SRL is much less sensitive to optical feedback, which is confirmed by a 25-dB weaker self-mixing signal. With a sufficiently strong strength, the SRL gives SW switching when subject to counter-directional delayed mutual feedback. The switching time and electrical linewidth of the SWs can be respectively reduced to 1.4 ns and 1.1 kHz by strengthening the feedback. The duty cycle can be tuned from 23% to 77% by adjusting the feedback delay times. High-order SWs can be observed for up to an order of 13, hereby circumventing the practical difficulties in realizing short delay paths for generating fast SWs. With the improved understanding on the time-delay characteristics of semiconductor lasers with optical feedback, their temporal waveforms can be applied in generating random bits, broadband signals, and SWs for the future applications.