For gravies, I use a little extra onion and some stick celery. Brown meat, sweat or brown onion/celery mix, cook. Then I remove meat and blend the onion/celery mix very well. You get a thicker sauce without use of any flour.
This works for some soups as well. You may blend some of the cooked vegetables, use some to have some "bite". I also use potatoes to cook along and then blend. I often opt for as little liquid to cook as possible, adding liquid (water, cream, etc) at the end. Seasoning at last when I have the consistency I like.
Note: if using carrot to cook along, make sure you remove carrot pieces before blending. Otherwise the taste of carrot owerpowers all else.