Current feedback (CFB) amplifiers mostly belong in the realm of high speed amplifiers. There are lot of good application notes developed over the years that describe the operation and the main issues encountered when applying current feedback amplifiers to a problem. Here we’ll try to summarize them in a few good words.
A CFB amplifier has one high impedance input (the non-inverting input), one low impedance input (the inverting input), and one output low impedance, as is represented below. Note that for the purpose of this discussion, I will be ignoring the power supply pin and disable functions.
Figure 1: CFB internal elements
The voltage on the non-inverting input sees a high input impedance so as not to load the input. The voltage on the non-inverting input appears on the inverting input as it passes through a buffer. As the buffer is non-ideal, it will have a gain a(s) that varies with frequency with DC magnitude very close to 1V/V but typically 0.996V/V. The buffer also ideally has output impedance equal to 0W. In practice, the output impedance varies between a few ohms to a few tens of ohms. I will also ignore the inductive component of that resistance as well for now.
The intent for the buffer is two-fold:
1) It forces the inverting node voltage to follow the non-inverting input.
2) It provides a low impedance path for the error current to flow.
As the error current passes through the buffer it is sent to the output through a high-transimpedance gain stage. Closing the feedback loop will drive the error current to almost zero in a fashion similar to the error voltage being driven to zero in a voltage feedback amplifier.
The only action left is to write the equation and interpret it.
is the noise gain, and in the case of the non-inverting configuration shown, the signal gain as well.
The loop gain can be expressed as:
This is a very important equation for an ideal CFB 
as it expresses the loop gain is proportional to the feedback resistance hence the feedback resistance is acting as the main compensation for CFB. In effect, increase the feedback resistance and the bandwidth (BW) will decrease the feedback resistance, while increasing the BW. In practice, it is not possible to reduce the feedback resistance below a certain value otherwise the amplifier will oscillate.
As long as 
, the BW, is not proportional to the gain, the CFB is considered fain-bandwidth product independent. In practice this is true to the first order as 
.
CFB will also have a naturally high slew rate and low bias current. The input stage is a buffer and provides as much current as it can until the internal transistors saturate. This saturation happens much later than traditional differential pair input voltage feedback amplifiers (VFB). That characteristic is very important and translates to much higher full power BW.
To conclude, CFB is not meant for every application. They fit best in applications that are most affected by increase in noise gain and where limited BW (a few 100MHz) but where high gain is needed. The CFB most likely is not used as the front-end amplifier as the VFB tends to do better due to lower noise. But as a second stage, they do offer a much better BW to quiescent current ratio than any VFB. CFB also does better in summing application where several inputs are required. In such applications, VFB’s BW will be limited by the noise gain. The last application in which CFB is most useful is line driver, where typically high gain and high BW are required simultaneously but also have high output current and high slew rate.