Some minor cracks and chips in a concrete driveway or walkway are not outside the area of expertise of most homeowners; there are concrete patch kits you can get from a hardware store and mix up in a large bucket and some that come in a tube for very small cracks. However, even with these materials available, this doesn't mean you should try to tackle all concrete repairs on your own. There are some that are going to be more difficult to fix than you realise and which should be left to a professional; note a few factors to consider so you know your property is always safe and in good repair.
Cracks that are wider at the top
When concrete has cracked in such a way that the crack is wider at the top than the base, it's good to actually chip away at the bottom of the crack with a chisel and sledgehammer. A wider base gives concrete filler a chance to settle and form a good foundation for the material. Knowing how much concrete to remove for a good shape you will fill in, without doing more damage to the material, can be a challenge. If not done right, you might split the concrete even further or not create enough of a wide V-shape for the filler.
If you need to repair the edge of a step, this too is more complicated than just putting on some putty or filler. An edge should use a form, usually a board that you attach to the step with a concrete screw. The new concrete is put over this board. If the board is not sized properly or attached to the step properly, your new concrete material might simply shift and sag or crack altogether, falling away from the old concrete. Remember that this can be very unsafe for steps, so this is best left to a professional.
When the concrete is sunk in one corner or side
If a concrete driveway or walk has cracked all the way through, you might be able to fill this with new concrete; if one side or corner is sunk, it will need to be braced up and made level and even. Remember that concrete filler and even fresh concrete is not meant to hold two pieces together. That repaired area will be weaker when one side or corner of concrete continues to sag and pulls on it, so have a contractor brace up the ground underneath before any repairs are made.