Spectroscopy is carried out in almost every field of science, whenever light interacts with matter1. Although sophisticated instruments with impressive performance characteristics are available, much effort continues to be invested in the development of miniaturized, cheap and easy-to-use systems1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Current microspectrometer designs mostly use interference filters2, 3, 4, 5 and interferometric optics3 that limit their photon efficiency, resolution and spectral range2, 3. Here we show that many of these limitations can be overcome by replacing interferometric optics with a two-dimensional absorptive filter array composed of colloidal quantum dots14, 15, 16, 17. Instead of measuring different bands of a spectrum individually after introducing temporal or spatial separations with gratings or interference-based narrowband filters, a colloidal quantum dot spectrometer measures a light spectrum based on the wavelength multiplexing principle18: multiple spectral bands are encoded and detected simultaneously with one filter and one detector9, 10, 11, 12, respectively, with the array format allowing the process to be efficiently repeated many times using different filters with different encoding so that sufficient information is obtained to enable computational reconstruction of the target spectrum. We illustrate the performance of such a quantum dot microspectrometer, made from 195 different types of quantum dots with absorption features that cover a spectral range of 300 nanometres, by measuring shifts in spectral peak positions as small as one nanometre. Given this performance, demonstrable avenues for further improvement, the ease with which quantum dots can be processed and integrated, and their numerous finely tuneable bandgaps that cover a broad spectral range, we expect that quantum dot microspectrometers will be useful in applications where minimizing size, weight, cost and complexity of the spectrometer are critical.