The physics of nanoscale devices has proven to be rich and interesting, both from the point of view of basic science and advanced technology. We study the physics of nanoelectronic and nanooptic devices for biomolecular sensing. Nanotechnology, with strong support from physics, has accelerated the development of a broad range of research fields, such as label-free biosensing where biomolecules need to be characterized and detected. Compared to established fluorescence-label based sensing methods, label-free methods have the advantage of being non-destructive, and are more suitable for newly emerging fields like proteomics. The key issue in developing label-free biosensors is to detect the biomolcules with high sensitivity and specificity. Nanoscale electronic and optic sensors show promising to satisfy these requirements. In developing nanoelectronic devices, we use a 'top-down' fabrication method to make silicon nanochannels with cross-section less than 100 nm by 100 nm, which can serve as the platform for highly sensitive detection of various chemical and biological molecules. In our systematic study, a model is developed to characterize electrical performance of the nanoelectronic field-effect transistor (FET), and the width dependent enhancement is demonstrated. These nanochannels have large surface-to-volume ratio compared to conventional large scale field-effect sensors, and thus have greater sensitivity to bimolecules bound to the device surface. Nanoelectronic sensors functionalized with chemicals and antibodies are shown to exhibit sensitivity at less than 1 nM to various biomolecules such as CA15.3, glucose, biotin, and to pH. In nanooptic biosensing research, we use theoretical models and simulations to study infrared surface plasmons. All biomolecules exhibit characteristic vibrational normal modes that can serve as the "fingerprint" of biomolecules. A 'top-down' fabrication method is used to fabricate metamaterials with designed infrared transmission properties, and our devices are tested with a Fourier transformed infrared (FTIR) micro-spectrometer over the frequency range 1000 - 4000 cm⁻¹. Our nanooptic biosensors are able to detect biomolecules by probing the enhanced intrinsic absorption of electromagnetic radiation for vibrational normal modes of biomolecules.