Fused silica exhibits high nonlinear optical response when exposed to ultrashort laser pulses, and the rapid development of femtosecond laser technology since the 1990s has greatly advanced the processing of such transparent materials. Since then, ultrafast laser micromachining has been widely implemented to remove materials or change material properties, from surface ablation to waveguide fabrication. Recently, we devised a potential use of this technique for optics precision correction of future space telescopes, for example the Lynx X-ray telescope mission. This novel mirror figure correction process provides a rapid and precise way of creating local micro deformation within the interior of thin mirrors, which then induces macro structural changes in surface figure to meet the stringent angular resolution requirements for the X-ray telescope. The method is highly controllable and deterministic, and the long-term stability of the laser-induced material changes makes it promising for future space telescope missions. In this paper, we review the mechanisms and nonlinear optical phenomena of femtosecond laser interaction with fused silica. We also report on the current development of our laser pulses generation, focusing, imaging and an in-situ wavefront sensing systems, as well as our procedure for measuring and correcting mirror substrates. Preliminary experimental results of local deformation and stress changes in flat thin fused silica mirror substrates are shown, demonstrating the correctability of fused silica substrates within a capture range of 1 µm in surface peak-to-valley or 200 in RMS slope using local laser micromachining. We also showed the laser induced integrated stress increases linearly with the micromachining density.