Here are some basic examples of caustics in Corona:
-there are two kinds of caustics: caused by refraction and caused by reflection, of course they mix on some materials
Refractive caustics:To get them to work, you need to check
"caustics (slow)" in your glass material's settings:
Max sample intensity (MSI) has impact on refractive caustics:

Caustics (slow) - MSI = 20 (default)

Caustics (slow) - MSI = 0
Default MSI value (20) produces less noise but "cuts off" some of the most intensive light passing through the object.
Higher MSI values or 0 will produce more realistic but much more noisy results.
If you
don't enable "caustics (slow)" in your glass material, you will get
transparent shadows. MSI has virtually no impact on transparent shadows (?). This can be considered "fake caustics":

No caustics (transparent shadows) - MSI = 20 (default)

No caustics (transparent shadows) - MSI = 0
If you
enable "thin (no refraction)" in your glass material, your glass won't change direction of light rays. It will behave like very thin material (for example light bulb, soap bubble, etc.):

Thin (no refraction) - MSI = 20 (default)

Thin (no refraction) - MSI = 0
You can also render caustics using
experimental features like VCM or BIDIR but they will most likely produce unusable results as they do not support some features like absorption:

VCM

BIDIR
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Reflective caustics:My metal material:
MSI also affects reflective caustics:

Reflective caustics - MSI = 20

Reflective caustics - MSI = 0
Reflective caustics also can be rendered using experimental engines:

VCM

BIDIR
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Whole album (with screenshots of some more settings):
[link]---
Note: currently, rendering of caustics of acceptable quality is very slow and usually it is recommended to use transparent shadows. For caustics lighting the whole room - like refractive caustics on the bottom of the swimming pool or reflective caustics from the surface of the water on the walls of the room, you can use CoronaLight with a bitmap assigned in its "texmap" slot. Caustics should work with both CoronaLights, standard Max lights, HDRI environment or other light sources.
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Comments/contributions welcome. :]