Multitude applications of photonic devices and technologies for the generation and manipulation of arbitrary and random microwave waveforms, at unprecedented processing speeds, have been proposed in the literature over the past three decades. This class of photonic applications for microwave engineering is known as microwave photonics (MWP). The vast capabilities of MWP have allowed the realization of key functionalities which are either highly complex or simply not possible in the microwave domain alone. Recently, this growing field has adopted the integrated photonics technologies to develop microwave photonic systems with enhanced robustness as well as with a significant reduction of size, cost, weight, and power consumption. In particular, silicon photonics technology is of great interest for this aim as it offers outstanding possibilities for integration of highly-complex active and passive photonic devices, permitting monolithic integration of MWP with high-speed silicon electronics. In this article, we present a review of recent work on MWP functions developed on the silicon platform. We particularly focus on newly reported designs for signal modulation, arbitrary waveform generation, filtering, true-time delay, phase shifting, beam steering, and frequency measurement.