Over time roots from trees or large shrubs can lift cement on walkways making them easy to trip over and dangerous. There are a number of choices on how to repair the problem, but they all start with removing the distorted surface concrete.
For small bumps, the surface of the concrete can be ground level. Builders codes require driveways in most cities to be at least six inches thick and three to four inches deep for patios and sidewalks. This should allow you to grind down an inch or two safely with a scarifier. Call in a professional if you are not comfortable with using a (rented or purchased) machine for the job. If the cement is being lifted by roots beneath, be prepared for the ground surface to continue to lift over time as the roots beneath continue to grow. The only way to keep this from happening is to remove the underlying cause all together.
Although you can create a step up or cut around a raised tree root, the safest walkway will be smooth and level. If you do not have space to route your path around the problem, the offending root will have to be cut and removed.
If there are sufficient chunks of concrete removed, you can repurpose them for building pedestals for pots, integrating in retaining walls, or setting into the ground as pavers. The hole will need attention next.
The space can be filled with a cement adhesive and concrete/polymer fill. Be prepared that this may chip away over time making it only a temporary patch. If a clean, even hole can be created, you can line it with rebar or wire hardware cloth and re-pour the cement to match surrounding areas.
There is another technique that is probably best given to professional specialists to handle when repairing pavement surface problems. If the surface concrete is intact and you don’t want to break it, you can remove the subsurface cause from the side and float the concrete back into position. This is accomplished by drilling holes in which cement is pumped to fill the hole beneath. The pressure of the added liquid beneath will float the existing slab back up to the surface. Floating concrete pavement is a better solution for areas where the pavement has sunk rather than lifted.