Multimode interference can be used to achieve ultra-high resolving powers (e.g., Q>105) with linewidths down to 10 pm at 1500 nm and a broad spectroscopy range (e.g., 400-2400 nm) within a monolithic, millimeter-scale device. For instance, multimode interference (MMI) in a tapered waveguide enables fine resolution and broadband spectroscopy in a compact, monolithic device. The operating range is limited by the transparency of the waveguide material and the sensitivity of the camera; thus, the technique can be easily extended into the ultraviolet and mid- and deep-infrared spectrum. Experiments show that a tapered fiber multimode interference spectrometer can operate across a range from 500 nm to 1600 nm (B=1.0576) without moving parts. The technique is suitable for on-chip tapered multimode waveguides, which could be fabricated in high volume by printing or optical lithography, for applications from biochemical sensing to the life and physical sciences.