what kind of grass is this?
I believe this is rough bluegrass (Poa trivialis aka roughstalk bluegrass). This is an introduced perennial cool-season grass.
Unfortunately there usually are no selective herbicides available to control cool-season grass weeds in a lawn. If the infestation(s) is small you can dig the grass out with a shovel, just make sure you go deep enough to remove the roots. I would also suggest making the hole wider than the infestation to make sure you get any of the creeping stems (stolons). You can then add soil and replant grass seed. If the infestation is larger you can use a nonselective herbicide, such as glyphosate (e.g. Roundup Weed and Grass Killer, though there are many others) to kill the grass, just keep in mind this will kill the lawn grass too. Repeat application may be needed, so you may want to wait at minimum of two weeks (in good, warm growing conditions) to make sure it has been controlled before replanting.
When using products containing glyphosate there are a few important points to consider. First, as with any pesticide, remember to read and follow all labeled instructions. Second, glyphosate is a broad-spectrum herbicide, meaning it will injure or kill other plants contacted during application, so care is needed to avoid green plant material, exposed roots, and injured bark of desired plants. Third, glyphosate is relatively safe in the environment when used as labeled. It adsorbs strongly to soil in most cases (i.e. clay and organic matter), allowing even sensitive crops to be planted shortly after application; meaning no carry over issues are expected. Fourth, glyphosate alone can take up to 14 days to show full activity under ideal growing conditions. Retreatment of the area may be needed depending on the degree of infestation. Glyphosate is most effective for perennial control in the fall but can be applied anytime the plants are actively growing (temperatures consistently above 50F). Finally, be sure that the product you choose has only the active ingredient glyphosate or glyphosate + pelargonic acid. Products with additional active ingredients may have other unwanted effects and may delay the planting of other plants in the coming season(s).
After you have achieved your desired level of control the work isn’t over. You need to do two important things. 1) Make sure you have a robust/vigorous stand of grass in your lawn to create a competitive environment for weeds. Practices could include re-seeding areas where the grass stand is thin, fertilizing the grass (early-spring and/or early-fall), watering when conditions are dry, and increasing your mowing height (~3.5", this last one will not help with tall fescue but will help with broadleaves and stress management). 2) You need to be on the lookout for weeds emerging from seed. Some weeds can linger as seeds in the “seed bank” of the soil for decades! Controlling these weeds could include the use of a preemergence herbicide (e.g. products targeting crabgrass control) or manual removal of emerged plants. More information on lawn care from the MSU Turfgrass Team can be found on the following website: https://www.canr.msu.edu/home_gardening/lawns/
Thanks for the answer, I think the best option here is to remove those patches of rough bluegrass I do not want to have more surprises with herbicide.