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The NASA Kepler mission obtained long-term high-quality photometric observations for a large number of stars in its original field of view from 2009 to 2013. To provide reliable stellar parameters in a homogeneous way, the LAMOST telescope began to carry out low-resolution spectroscopic observations for as many stars as possible in the Kepler field in 2012. By June 2018, 238 386 low-resolution spectra with SNRg ≥ 6 had been collected for 155 623 stars in the Kepler field, enabling the determination of atmospheric parameters and radial velocities, as well as spectral classification of the target stars.This information has been used by astronomers to carry out research in various fields, including stellar pulsations and asteroseismology, exoplanets, stellar magnetic activity and flares, peculiar stars and the Milky Way, binary stars, etc. We summarize the research progress in these fields where the usage of data from the LAMOST-Kepler (LK) project has played a role. In addition, time-domain medium-resolution spectroscopic observations have been carried out for about 12000 stars in four central plates of the Kepler field since 2018. The currently available results show that the LAMOST-Kepler medium resolution (LK-MRS) observations provide qualified data suitable for research in additional science projects including binaries, high-amplitude pulsating stars, etc. As LAMOST is continuing to collect both low- and medium-resolution spectra of stars in the Kepler field, we expect more data to be released continuously and new scientific results to appear based on the LK project data.