What kinds of organisms can perform photosynthesis? Which types of organisms cannot?

Most plants, most algae and cyanobacteria kinds of organisms (Autotrophs) can perform photosynthesis while heterotrophs are organisms incapable of photosynthesis.

Explanation:

Photosynthesis is a mechanism used among plants as well as other species to transform energy from the sun into chemical energy which may be released later to power the functions of the species.

In autotrophs (organisms who self prepare there food ) with the support of a subsequent series of light-independent reactions like Calvin cycle, creates long-term energy collection in the form of sugars, while some bacteria use different mechanisms like the reverse Krebs cycle to accomplish the same purpose.

Heterotrophs are entities unable to photosynthesize and, by eating certain species, must therefore obtain energy and carbon from the food. In the term heterotroph: hetero means "other" while troph means "feeder", thus their food depends on other species.

Phototropic organisms can preform photosynthesis.

Heterotrophic organisms  cannot perform synthesis

Explanation:

Phototrophs:

Heterotrophs: