Loop compensation of a Buck Converter
The loop compensation of the buck converter depends on many factors as you can imagine. Below are a few simple statements to help you narrow down your search and find the answers you are looking for:


control mode: it corresponds to the way you control the converter. There are many control schemes but the most popular are fixed-frequency voltage- or current-mode-control types. 
voltage-mode control (VM): the switching frequency \$F_{SW}\$ is fixed and the loop adjusts the duty ratio \$D\$ via a dedicated pulse width modulator (PWM). This is also known as direct duty ratio control.
current-mode control (CM): the switching frequency \$F_{SW}\$ is also fixed but the loop adjusts the inductor peak current, indirectly adjusting the duty ratio. Please note that \$D\$ is the same for a given operating point whether you operate the converter in VM or CM.
operating mode: a switching converter like a buck associates two energy-storing elements. Looking at the inductor current \$i_L(t)\$ tells you how the converter operates. If the inductor current does not return to zero during a switching cycle, the converter operates in continuous conduction mode or CCM. If the inductor current goes to zero and remains there for a given duration (deadtime), the converter operates in discontinuous conduction mode or DCM. Usually, a converter operates in CCM at high output current and transitions to DCM as the load is getting lighter.
loop response: this is the point of interest here. Before attempting to control a given switching converter and regardless of its operating mode or scheme, you must have on hand its control-to-output transfer function. That is to say, how a small variation (or perturbation) applied to the control variable (\$D\$ for instance) propagates through the power stage and creates an output response. A Bode plot will instruct you how the amplitude of the perturbation is affected (magnitude plot in dB) and how its phase is also impacted (phase plot in degrees). 


5a. VM: in VM, the buck transfer function is that of a second-order circuit affected by a resonant frequency and a quality factor. You must use a type 3 compensator in your compensation strategy (1 pole at the origin, 2 poles and 2 zeroes). When the buck transitions to DCM, the response becomes that of a 1st order circuit. Your compensation strategy must ensure a seamless transition between modes.

5b. CM: in CM, the power stage response is that of a 3rd-order circuit, A dominant pole in low-frequency and two high-frequency poles located at half the switching frequency. These two subharmonic poles must be damped with an artificial ramp for stability purposes. In light-load conditions, the CM converter remains a 1st order (the subharmonic poles are gone) and this makes the CM converter an easy-to-stabilize converter with a type 2 compensator (1 pole at the origin, 1 pole and 1 zero).

If you want to know more about the compensation of the buck converter, please have a look at this APEC 2019 seminar or study this book for an introduction to switching converters and their small-signal responses. Good luck with your design!