An LT1637 is advertised as 1.1MHz, 0.4V/us Over-The-Top Micropower, Rail-To-Rail Input and Output Op Amp. Since the input voltages are right at the upper rail, this features are suitable for current sensing applications. The schematic below shows current sensing of 5V supply system, and monitoring can be done up to 44V application. This is the maximum supply voltage of the op-amp.
The VOS performance of op amps at the supply is generally less accurate than other solutions, this is because it is not factory trimmed. A small source of gain error is introduced by the finite current gain of the bipolar transistor. [Source: Linear Technology Application Notes]