Buck converter

A buck converter (step-down converter) is used when a lower output voltage than a input voltage is needed.This basic topology is used for the SMPS which requires multiple outputs and this is also used for secondary DC/DC converter generally.

Isolated fly-back converter

An isolated fly-back converter can be implemented at low cost and typically used for AC/DC converter of power converter up to 150W.
The switching element transfers energy to the load during the off time of the primary side.

PFC boost converter

A PFC boost converter is used for producing a higher output voltage than a input voltage through increasing the input voltage.
This is used for supplying DC power and most commonly used for AC/DC SMPS over 100W needed active PFC (Power Factor Correction).

Half-bridge converter

A half-bridge converter is used for power supply of 150 ~ 1,000W.
This topology uses a transformer and an output inductors along with a forward converter.
However the transformer of a half bridge converter can use more capacity using the transformer and the output inductor.
And two MOSFETs work separately with a dead time between the two MOSFETs.