Integrated nanophotonic circuits allow for realizing complex optical functionality in a compact and reproducible fashion through high-yield nanofabrication. Typically configured for single-mode operation in a single path, the optical propagation direction in such devices is determined by the waveguide layout which inherently requires smooth surfaces without scattering and restricts the device footprint to the limits of total internal reflection. Yet intentionally introducing disorder and scattering can be beneficial for the realization of novel nanophotonic components to overcome fabrication imperfections. Therefore, the understanding of the underlying physics of randomly disordered nanophotonic systems has gained increased attention. In particular on-chip spectrometers may benefit from random disorder. These devices are widely used tools in chemical and biological sensing, materials analysis and light source characterization. Conventional nanophotonic spectrometer designs are based on concepts using ring resonators, arrayed waveguide gratings or echelle gratings. Those devices are based on careful design and rely on high control of the fabrication and are therefore prone to fabrication errors and exhibit a very large footprint. Here, as part of the priority program “Tailored Disorder” (SPP 1839), we utilize multi-path interference and the interaction of light with randomly oriented scatterers to realize broadband and narrow linewidth on-chip integrated spectrometers with small footprint. In combination with integrated superconducting nanowire single-photon detectors such devices allow for resolving optical spectra on the single photon level which is of interest for single-photon spectroscopy or quantum wavelength division multiplexing.