The next generation of Extremely Large Telescopes (ELT), with diameters up to 39 meters, will start opera- tion in the next decade and promises new challenges in the development of instruments. The growing field of astrophotonics (the use of photonic technologies in astronomy) can partly solve this problem by allowing mass production of fully integrated and robust instruments combining various optical functions, with the potential to reduce the size, complexity and cost of instruments. In this paper, we focus on developments in integrated micro-spectrographs and their potential for ELTs. We take an inventory of the identified technologies currently in development, and compare the performance of the different concepts. We show that in the current context of single-mode instruments, integrated spectrographs making use of, e.g., a photonic lantern can be a solution to reach the desired performance. However, in the longer term, there is a clear need to develop multimode devices to improve overall the throughput and sensitivity, while decreasing the instrument complexity.