The problem most programmers would be familiar with is making an update inside a deeply nested immutable data structure. For example, suppose you want to update a user's billing address, and you have an immutable data structure that looks like this:

    user { billingInfo: { card, address }, name, subscription { level, expiration }, status { level, since } }

The structure is immutable, so you can't make the update in place. On the other hand, you're only changing one field, so it would be wasteful to make a complete deep copy. The efficient way to create an updated instance is to create a new user instance and a new billingInfo instance while reusing the name, subscription, and status instances.

You can think of this as the equivalent of a setter for immutable data structures.

This is an artificial example, because the cost of making a deep copy of this user structure is probably not that bad, and the boilerplate to make an efficient update is not all that bad, either. You would use an optics library when 1) you need efficient updates and 2) it's worth investing a little effort to hide the boilerplate.

Optics also let you concisely express access into a deeply nested structure, the getter paired with the setter. In my experience, updates are the motivation for setting up optics, and concise access is a nice thing you get as a bonus.

If monads are programmable semicolons (ways to chain operation), lenses are programmable dots (ways to delegate access to data). Other optics are largely generalizations of that pattern.

Lens are the functional version of getters and setters. A lens takes a product type (struct, class, etc) and allows you to view or update part of it. Prisms are something similar for sum types (variants) that allow you to look at a value if it's present and err otherwise.

The optical analogy comes from how these operations resemble zooming in on structures with a magnifying glass and the entire family of related transformations is called optics.

Aside from making it convenient to build getters and setters for nested data, optics also have conditional accessors and collection accessors as building blocks.

Conditional accessors have since become a popular language feature with e.g. the elvis operator ?. in C#. Optics make it possible to innovate on features like that in library code rather than as language features.

Something I've yet to see made into a language feature that is common in optics libraries are iterating accessors. E.g. to reset all counters we can, with optics, say something like (in Haskell syntax, since that is what I know)

    stats.each.count .= 0

and that sets the count to zero for all objects in the stats array. If not all stats objects have a count (some might be of a gauge type, for example) we can compose in a conditional accessor that resolves the count field only if it is not null:

    stats.each.count._Just .= 0

In the above statement, nothing is language syntax --it's all library functions and operators. But it still combines really well on the page. Once one knows optics, one rarely has to think very hard about how to do any get or update operation, even when the data types become complicated.

Lenses make it easier to read and update members deep in a hierarchy of read-only data structures.

There's one book that discusses a few related questions from a very mainstream perspective: Functional and Reactive Domain Modeling (https://www.manning.com/books/functional-and-reactive-domain...). The emphasis here is on practical while most similar resources tend to go too hard in the Haskell-on-the-JVM direction.