If it can be repaired economically that is what they will do. If you have "New for Old " in your policy terms then if it is beyond repair they will replace it. If you do not have the "New for Old " feature then you may receive a cash payment but this will be lower than the replacement value as they will take into account depreciation.
i think it depends on the item and the insurance company as to what they do, but make sure its worth claiming for, i claimed earlier this year for something and then when my insurance was up for renewal they had tripled the quote because id claimed