They are also sometimes thought of as a neuronal network or fragment of memory, sometimes using a hologram analogy to describe its action in light of results showing that memory appears to be non-localized in the brain. The existence of engrams is posited by some scientific theories to explain the persistence of memory and how memories are stored in the brain. The existence of neurologically defined engrams is not significantly disputed, though its exact mechanism and location has been a persistent focus of research for many decades.
The term engram was coined by relatively unknown but nevertheless influential memory researcher Richard Semon.
Karl S. Lashley's "search for the engram" found that the engram did not exist in a specific part of the brain, but discovered that memory was widely distributed throughout the cortex. One possible explanation for Lashley's failure to locate the engram is that many types of memories (eg. visuo-spacial, smell, etc.) are used in the processing of complex tasks such as rats running mazes. Now the general view in neuroscience is that memory involved in complex tasks is distributed across multiple neural systems. At the same time, certain types of knowledge are processed and contained in specific brain regions. Overall, the mechanisms of memory are not well understood. Brain areas such as the cerebellum, striatum, cerebral cortex, hippocampus, and the amygdala are thought to play an important role in the memory. For example, the hippocampus is believed to be involved in spatial learning and declarative learning.
In Lashley's experiments (1929, 1950), rats were trained to run mazes then the experimenter remove tissue from the rats cortex and ran them through the same maze to see if their memory would be affected. It was found that increasing the amount of tissue removed further degraded the rats memory. More importantly where the tissue was removed from made no difference to the rats memory of the maze.
Later researcher, Richard F. Thompson, sought the engram of memory in the cerebellum instead of the cerebral cortex. Thompson and his colleagues used classical conditioning of the eyelid response in rabbits in their search for an engram. They puffed air upon the cornea of the eye and paired it with a tone. This airpuff normally causes an automatic blinking response. After a number of trials they conditioned the rabbits to blink when they heard the tone even though the airpuff was no longer administered. During the experiment, they monitored several brain cells to try to locate the engram.
One brain region that Thompson's group monitored that they thought was a possible part of the memory engram was the lateral interpositus nucleus (LIP), when chemically deactivated, it resulted in the rabbits, who were previously conditioned to blink when hearing the tone, to act as if the conditioning never took place; however, when they re-activated the LIP, they responded to the tone again with an eyeblink. This gives evidence that the LIP is a key element of the engram for this behavioral response. 
It is important to stress that this approach targeting the cerebellum, though relatively successful, only examines basic, automatic responses. Almost all animals have these (especially as defense mechanisms) and it is fairly difficult to resist them.
Ideally, research by Thompson and others could eventually lead to isolation of more complicated engrams that control more abstract, declarative memories, like how one remembers one's name or the capital of France. Engrams could also explain why users of psychedelic substances experience "flashbacks", which are probably caused by their endogenous dimethyltryptamine, mostly produced in the pineal gland, because resemblances to previous spiritual experiences in their environment seem to trigger these effects.
The problem here is that considerable studies have shown declarative memories tend to move about the brain between the limbic system (deep within the brain) and the outer cortical areas. This contrasts with the more "primitive" set-up of the cerebellum, which controls the blinking response and receives direct input of auditory information. Thus, it does not need to reach out to other brain structures for assistance in forming simpler memories of association.
- Forgotten Ideas, Neglected Pioneers: Richard Semon and the Story of Memory, Daniel Schacter, 2001 ISBN 184169052X