Infrared (IR) sensors and photodetector arrays are employed in various imaging applications (such as night vision), remote temperature measurement, and chemical analysis. These applications are in space and environmental sensing, transport, health and medicine, safety, security, defense, industry, agriculture, etc. Optical chemical analysis employs IR absorption spectroscopy which enables the identification and quantification of gases, liquids, and materials based on their unique absorption spectra which are feature-rich in the IR region. State-of-the-art (SoA) quantum photodetectors utilize either photoconductivity or the photovoltaic effect. Commercial quantum photodetectors are widely available in the spectral range from UV to short-wave infrared (SWIR), but in midwave IR (MWIR) and long-wave IR (LWIR), they require exotic materials and cooling to maintain high sensitivity. Thermal detectors (bolometers) are a competing technology that can reach high sensitivities in IR without the need for cooling and can be manufactured using widely available semiconductor technologies. SoA bolometers include resistive bolometers, diode- or transistor-based bolometers, and thermoelectric bolometers. By utilizing nanomaterials and integrated design, we have minimized the thermal mass and demonstrated fast and sensitive nano-thermoelectric IR bolometers with high thermoelectric efficiency. We review the application and development of the silicon-based nano-thermoelectric infrared bolometers: modelling, design, fabrication, and electro-optical characteristics. The enabling materials, silicon nanomembranes, are also discussed, and the first devices used to test the potential of these nanomembranes, the electro-thermal devices, are reviewed and new experimental results are presented.