Then there are those who have no conseptual understanding of just what depreciation really is, and an even less understanding of the difference between capitalization/capitalized costs, and amortization/amortized cost. So here's the simplicity of it.
Cost associated with the acquisition of the property are capitalized and depreciated over time. For example, title transfer fees paid at the courthouse to change the title of the property into the buyer's name.
Cost associated with the acquisition of the loan used to purchase the property, are amortized and deducted over time. As an example, loan application fees and points paid on the loan. (Points are basically pre-paid interest that is paid in advance, but can also include other expenses associated with the loan.) For rental property, these costs are deducted over the life of the loan.
So depreciation reduces your cost basis in the asset, while amortization reduces the amount of income made with that asset, that is taxable.
It's an odd setup, as if you have a 15 year loan your amortized cost will be completely deducted before the property is completely depreciated. If it's a 30 year loan, the property will be completely depreciated a few years before all of your amortized deductions are realized.
One good thing about the amortized deductions, is that if you sell the property and pay off the loan with the sale proceeds, any remaining amortized amounts left are deducted in the year you sell. Likewise, if you refinance the property to a new loan (so long as it's not with the same lender) then you can deduct the remaining amortized costs on the old loan, and start them anew with your amortized cost incurred in acquiring the new loan.
