That school of thought was created by psychologists interested in perception, especially visual perception. Its most basic principles are two:
1. A form, structure or Gestalt is defined, perceived and remembered by the pattern of relations between its elements or parts, and not reducible to them.
2. The whole is other than the sum of the parts, and not reducible to them.
These principles are not just useful but indispensable to understand, among other things, perceptual constancy (a rose is a rose, is a rose, despite differences in size, fragrance, color, etc..). They are indispensable to understand the essentials of language and every other cognitive function.
They are also indispensable to understand the structure and dynamics of neural networks, in the brain or out of it. The reason they are indispensable is because the cognitive code is essentially a relational code at all levels of analysis.
Essentially the concepts of Gestalt are--or should be--given preeminence in the neuroscience of attention, perception, memory, language and intelligence. The connectome--if we ever get it!--will make no sense to anyone without the Gestalt principles.
My explanation for the prevailing neglect is simply that Gestalt is essentially antithetical to reductionism, the "golden rule" of natural science. This makes it difficult to handle by the computational neuroscientist.
Yet people should learn, the sooner the better, that there is a methodological "floor" to cognition and to cognitive neuroscience. Reductionism under that "floor" is pointless and self-defeating. A percept, a memory, a word, a sentence, a cortical neural network,...disintegrate, their meaning and function lost, if we attempt to pierce that floor with our obstinate reductionism.
Cheers, Joaquín