Photonic signal processing has been considered a promising solution to overcome the inherent bandwidth limitations of its electronic counterparts. Over the last few years, an impressive range of photonic integrated signal processors have been proposed with the technological advances of III-V and silicon photonics, but the signal processors offer limited tunability or reconfigurability, a feature highly needed for the implementation of programmable photonic signal processors. In this thesis, tunable and reconfigurable photonic signal processors are studied. Specifically, a photonic signal processor based on the III-V material system having a single ring resonator structure for temporal integration and Hilbert transformation with a tunable fractional order and tunable operation wavelength is proposed and experimentally demonstrated. The temporal integrator has an integration time of 6331 ps, which is an order of magnitude longer than that provided by the previously reported photonic integrators. The processor can also provide a continuously tunable fractional order and a tunable operation wavelength. To enable general-purpose signal processing, a reconfigurable photonic signal processor based on the III-V material system having a three-coupled ring resonator structure is proposed and experimentally demonstrated. The reconfigurability of the processor is achieved by forward or reverse biasing the semiconductor optical amplifiers (SOAs) in the ring resonators, to change the optical geometry of the processor which allows the processor to perform different photonic signal processing functions including temporal integration, temporal differentiation, and Hilbert transformation. The integration time of the signal processor is measured to be 10.9 ns, which is largely improved compared with the single ring resonator structure due to a higher Q-factor. In addition, 1st, 2nd, and 3rd of temporal integration operations are demonstrated, as well as a continuously tunable order for differentiation and Hilbert transformation. The tuning range of the operation wavelength is 0.22 nm for the processor to perform the three functions. Compared with the III-V material system, the CMOS compatible SOI material system is more cost effective, and it offers a smaller footprint due to the strong refractive index contrast between silicon and silica. Active components such as phase modulators (PMs) can also be implemented. In this thesis, two photonic temporal differentiators having an interferometer structure to achieve active and passive fractional order tuning are proposed and experimentally demonstrated. For both the active and passive temporal differentiators, the fractional order can be tuned from 0 to 1. For the active temporal differentiator, the tuning range of the operation wavelength is 0.74 nm. The use of the actively tunable temporal differentiator to perform high speed coding with a data rate of 16 Gbps is also experimentally demonstrated.