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In this thesis, material and device characterizations are reported for Si$\sb{1-x}$Ge$\sb{x}$ alloys and Si$\sb{1-x}$Ge$\sb{x}$/Si heterostructures. Among the characterizations transmission electron microscopy of the MBE grown Ge-rich heterostructures investigates the dislocation formation and propagation to identify an effective dislocation trapping buffer layer for device applications. SiGe/Si, p - i(Si$\sb{1-x}$Ge$\sb{x}$) - n photodiodes are designed, fabricated and characterized for the spectral response in the wavelength region of 0.6$\mu$m to 1.6$\mu$m. The cut-off wavelengths are presented for the entire composition range of 0.08 $\le x \le$ 1. From photocurrent multiplication factors, the impact ionization coefficients, $\alpha$ and $\beta$ are measured for the first time in relaxed Si$\sb{1-x}$Ge$\sb{x}$ alloys. The $\beta/\alpha$ ratio, which is very important in the design of low noise avalanche photodiode, is reported as a function of Ge compositions as well. In addition, SiGe/Si heterojunction bipolar transistors are designed and fabricated by using a new selective wet chemical etchant of Si with respect to SiGe, tetramethyel ammonium hydroxide. For the optical characterizations, the photoluminescence studies on SiGe/Si quantum structures and the measurement of electro-optic coefficients in Si$\sb{1-x}$Ge$\sb{x}$ alloys are presented. Some enhancement in photoluminescence and the quantum confinement effect are observed in SiGe/Si multiquantum wells (MQW), disordered MQWs and disordered quantum wires. A large electro-optic effect in Si$\sb{1-x}$Ge$\sb{x}$ and an attempt to measure this effect are reported by using Si$\sb{1-x}$Ge$\sb{x}$/Si ridge waveguides with asymmetric quantum wells in the active region.