Many people are not aware of this, but repairing sidewalks is an important step in maintaining the safety of your home.
You should know that there are two different types of repair methods: surface and structural.
Surface repairs are for damage to the top layer of concrete such as cracks and chips. These usually require only a sealant or a new coat of paint to fix. This type of repair is cheaper and can be done by yourself with little effort. Over at this old house there is a great article on concrete sealants you might want to consider for the job.
Structural repairs on the other hand, are for damage underneath the surface such as broken or sunken concrete slabs, missing sidewalk panels, or cracks that go deeper than the top layer. These usually require more time, money and expertise to fix due to their complexity.
Repairing a concrete sidewalk can be a difficult process because the concrete must be removed in order to reach the damaged area. The best repairs are likely to be found by removing the damaged section, examining it and then choosing how to re-pour the concrete.
Everyday Home Repairs has an excellent video on how to fix a large crack in a concrete sidewalk here.