To keep pace with the ever-increasing demand of integration and miniaturization, it is imperative to redesign conventional optical systems and components and develop new compact ones. Optical spectrometers have been widely adopted as powerful analytical tools showcased by a plethora of applications ranging from medical diagnostics and food analysis to gas and bio-agent sensing and environmental monitoring. Conventional spectroscopy tools require bulky and expensive optical elements, with electronics that result in benchtop systems with limited scope for portability. On-chip spectrometers, on the other hand, are alignment-free and lightweight devices that, unlike their commercially available off-chip counterparts, offer sensing in portable applications and make at-the-sample analysis possible. In this dissertation, chip-scale optical spectrometers with different working principles are studied and implemented. First, an efficient mid-infrared polarization rotator in silicon-on-sapphire is experimentally demonstrated. Since the emission from quantum cascade laser sources is transverse magnetic polarized, this component can be used to convert the polarization state of the light source and couple it into transverse electric photonic components. In chapter 3, we experimentally demonstrate an on-chip Ethyl alcohol sensor based on a holey photonic crystal waveguide on a silicon on insulator platform, offering an enhanced absorption enabled by a slow-light mode and enhanced optical field intensities in the waveguide. In chapter 4, a surface-normal hollow-core photonic crystal waveguide sensor is introduced with a geometry similar to photonic bandgap fibers with perfectly periodic air holes as cladding in a 2-dimensional photonic crystal arrangement that gives rise to bandgaps at specific frequencies and a central defect for strong modal field confinement. On account of the slow-light effect, this device offers a high degree of dispersion control and can be employed for multi-gas detection. Finally, in chapter 5, we present two different devices with single channel geometries that can be used for on-chip spectroscopy. In the first part of this chapter, we present the design and implementation of a cascaded microring-MZI device as a platform for Fourier transform spectroscopy in O-band. In the second part, we demonstrate a device with finely tunable cascaded microdisks offering a platform for on-chip spectroscopy in C-band. Optical devices presented in this dissertation provide a path toward high-performance integrated spectrometers with subcentimeter-scale footprints that enable handheld spectral analysis and more real-life applications