Spectroscopic analysis is one of the most widely used analytical tools across both scientific research and industry. Whilst laboratory bench-top spectrometer systems offer superlative resolution and spectral range, their miniaturization is crucial for applications where portability is paramount, or in-situ measurements must be made. Advancement in this field over the last three decades is now yielding microspectrometers with performance and footprint near those viable for lab-on-a-chip systems, smartphones and other consumer technologies. In this review, we briefly summarize the technologies that have emerged toward achieving these aims - including miniaturized dispersive optics, narrowband filter systems, Fourier transform interferometers and reconstructive microspectrometers - and discuss the challenges associated with improving spectral resolution while device dimensions shrink ever further.