[Note: Acute means sudden onset, chronic means has lasted a long time]
Putting ice onto an acute injury is common practice. One rationale behind this is that the ice reduces swelling. However there has been substantial research and it has not shown a conclusive effect for icing. Whereas there is strong evidence that compression is effective in reducing swelling.
So is ice redundant?
Not at all – lowering the temperatures of the effected area reduces pain. Ice is cold. So in the first few hours after injury repeated ice treatment could reduce the level of pain and help make the injury feel better sooner.
When applying a bandage for compression you can apply crushed ice at the same time. Don't apply the ice directly to the skin or you may cause an ice burn. Alternate ten minutes compression with ice and ten minutes compression without ice, for as long as possible immediately after injury.
Another technique is ice immersion. Over the following days and weeks immersion can play an important role in rehabilitation by getting you moving and working the injured area. Early movement helps reduce swelling as the muscle contractions pump out the fluids associated with the swelling. It also enables you to regain full pain-free movement quicker.
For ice emersion you place the injured area into cold water with a few ice cubes for about 20 minutes. When the area feels numb you can start moving the affected joint or muscle.