Nonlinear dynamical properties of semiconductor lasers have attracted considerable attention, and their rich behaviors enable many popular research topics. The research effort of this thesis has emphasized on two areas - one is photonic microwave generation based on period one dynamic of semiconductor lasers; the other is laser's chaotic dynamic. Microwave photonics has attracted considerable attention recently because of its practical applications in radio-over-fiber (RoF) communications links. A stable photonic microwave allows it to convey, in a cost-effective manner, wideband signals over optical fibers with low loss, large bandwidth and immunity of electromagnetic interference. Microwave photonics technologies consist of photonic microwave generation, processing, control and distribution. Many photonic microwave generation techniques have been proposed, which includes direct modulation, optical heterodyne technique, external modulation, mode-locked semiconductor lasers, optoelectronic oscillator (OEO) and period one (P1) dynamic of semiconductor lasers. Among these techniques, photonic microwave generation based on P1 oscillation dynamic has gained special attention due to its many advantages, such as: widely tunable oscillation frequency, and nearly single sideband (SSB) spectrum. The aim of this thesis in the photonic microwave generation area is to produce photonic microwaves based on P1 dynamic using low-cost vertical-cavity surface-emitting lasers (VCSELs). The technical contents in this area cover two parts. The first part is to generate broadly tunable photonic microwaves. Continuous tuning of the microwave frequency from 4GHz to up to an instrumentation limited 15GHz is experimental achieved through the adjustment of the injection power and the frequency detuning between the master laser and the VCSEL. Numerical simulations using a common spin flip model are also carried out, which agree qualitatively with the experimental results. The second part of the photonic microwave generation in this thesis is to explore effective approaches to not only reduce the linewidth but also improve the stability of the generated microwave. Due to spontaneous emission noise in the semiconductor laser, P1 dynamic inherently imposes phase noise, which increases the microwave linewidth of the generated microwave. This considerably affect the signal transmission performance of the modulated microwave signal in RoF applications. To address this challenge, single optical feedback and double optical feedback are applied in the experiments. The experimental results demonstrate that both single feedback and double feedback can reduce the linewidth of the generated microwave to about one tenth of linewidth without the optical feedback. However, single optical feedback may induce many side peaks due to external cavity frequency from the feedback cavity, the feedback phase needs to be carefully adjusted to suppress the side peaks. The side peaks can be suppressed by introducing the second optical feedback. The double optical feedback can also significantly enhance the stability of the generated microwave. The results of the numerical simulations are in good agreement with the experimental results. The other important dynamic of semiconductor lasers is chaos, which has attracted considerable research interest due to its many potential applications in secure communications, chaotic optical time-domain reflectors, chaotic lidars and physical random number generators. Optical feedback is the simplest method to generate chaos in semiconductor lasers, but a typical chaos generated by optical feedback has unwanted recurrence features termed time delay (TD) signature because of the optical round trip in the external cavity. The complexity, bandwidth and TD signature of chaos are the three main parameters for evaluating its applicability in abovementioned application scenarios. In order to find the correct operating parameters to achieve low TD signature and high complexity of chaos simultaneously, in this thesis, the influence of bias current and the feedback strength on the complexity and time-delay signature of chaotic signals in semiconductor lasers with optical feedback is investigated experimentally and theoretically. In the experiment, the effect of the data acquisition method on quantification of complexity is also examined. The experimental results show that the TD signature is approximately in an inverse relationship with the complexity of chaos when the semiconductor laser is subject to low or strong optical feedback. However, the inverse relationship disappears when the laser operates at higher bias currents with intermediate feedback strength. Numerical simulation based on Lang Kobayashi laser equations show qualitative agreements with the experimental results.