Silicon photonics has emerged as one of the most popular areas in integrated optics because of its compatibility with CMOS fabrication processes and its potential for low cost and mass production. To enable efficient fiber-to-chip coupling of light, one key component is a grating coupler. With an increasing demand for wavelength-division-multiplexing systems in fiber-to-the-home network services, low-cost dual-band (O- and C-bands) chip transceivers are required. In this thesis, the universal design methodology of conventional and subwavelength grating couplers has been presented. Firstly, a vertical incident wavelength splitting grating coupler that can split 1310 nm and 1550 nm wavelength light into two directions is shown. Afterward, a polarization splitting grating coupler that can work for both C- and O- band with a flexible incident angle is also demonstrated. In the last part of this thesis, a novel dual-band subwavelength polarization independent grating coupler works as a wavelength demultiplexer is proposed.