Concrete that has been installed correctly can hold up well over time. If it was not mixed according to directions, or if the wrong materials were used, then eventually you will see cracks, chips and crumbling. Tearing out concrete is difficult. If you don't have the time or money to do that, you can resurface the concrete with a specialized layer of concrete resurfacer, called an overlay. This concrete resurfacer is a thin layer of a polymer-based cement that will make the surface like new. You can buy pre-made mix or make it yourself. The trick is making it correctly.
Mix the dry ingredients including 2 1/2 parts of cement-grade sand with 1 part cement if you don't want to use a premixed polymer-based cement. If you want to put a gravel or stone in the overlay mix, stir together 2 parts stone or gravel with 1 part sand and cement. Use a large container or wheelbarrow to mix the cement.
Mix up a cement "paint" in a separate bucket. Use 1 part cement and 1 part sand. Add water to the mix until it is the consistency of paint. This is used to coat the surface of the concrete right before you do the overlay coat. The mixture is thin enough to get down into the pores of the old concrete, as well as bond to the new.
Mix up the pre-made polymer concrete according to the directions on the package, or for mixes you made yourself in Step 1, add water slowly while stirring until you get the proper consistency. Whether you made it yourself or use the pre-made mix, you want it to be spreadable, but not have so much water in it that it can be poured. You want it to be somewhat thick, but not so much that it is moldable.
Paint on the cement paint that you mixed in Step 2. Paint it over the entire surface with a paintbrush. It will dry fairly quickly, and is meant to get down in the pores of the old cement and give the new mix something to adhere to. Once the paint is on, spread the mixture -- either the polymer base or the homemade mixture -- onto the concrete. It is best to build a wood frame around the surface to give form to the new material. Spread it smooth with a trowel. The polymer base is generally a little more fluid than the homemade mixture, and it creates a smoother surface.