This paper reviews architectures and circuit implementations of on-chip sinusoidal signal generators (SSGs) for electrical impedance spectroscopy (EIS) applications. In recent years, there have been increasing interests in on-chip EIS systems, which measure a target material's impedance spectrum over a frequency range. The on-chip implementation allows EIS systems to have low power and small form factor, enabling various biomedical applications. One of the key building blocks of on-chip EIS systems is on-chip SSG, which determines the frequency range and the analysis precision of the whole EIS system. On-chip SSGs are generally required to have high linearity, wide frequency range, and high power and area efficiency. They are typically composed of three stages in general: waveform generation, linearity enhancement, and current injection. First, a sinusoidal waveform should be generated in SSGs. The generated waveform's frequency should be accurately adjustable over a wide range. The firstly generated waveform may not be perfectly linear, including unwanted harmonics. In the following linearity-enhancement step, these harmonics are attenuated by using filters typically. As the linearity of the waveform is improved, the precision of the EIS system gets ensured. Lastly, the filtered voltage waveform is now converted to a current by a current driver. Then, the current sinusoidal signal is injected into the target impedance. This review discusses the principles, advantages, and disadvantages of various techniques applied to each step in state-of-the-art on-chip SSGs. In addition, state-of-the-art designs are compared and summarized.