The development of optical fibers has revolutionized telecommunications by enabling long-distance broadband transmission with minimal loss. In turn, the ubiquity of high-quality, low-cost fibers has enabled a number of additional applications, including fiber sensors, fiber lasers, and imaging fiber bundles. Recently, we showed that a multimode optical fiber can also function as a spectrometer by measuring the wavelengthdependent speckle pattern formed by interference between the guided modes. Here, we reach a record resolution of 1 pm at a wavelength of 1500 nm using a 100 m long multimode fiber, outperforming the state-of-the-art grating spectrometers. We also achieved broadband operation with a 4 cm long fiber, covering 400 - 750 nm with 1 nm resolution. The fiber spectrometer, consisting of the fiber, which can be coiled to a small volume, and a monochrome camera that records the speckle pattern, is compact, lightweight, and low cost while providing ultrahigh resolution, broad bandwidth, and low loss. (C) 2014 Optical Society of America