Most of the time, we think in terms of types with a fixed, positive size. This is not always the case, however.

Rust in fact supports Dynamically Sized Types (DSTs): types without a statically known size or alignment. On the surface, this is a bit nonsensical: Rust must know the size and alignment of something in order to correctly work with it! In this regard, DSTs are not normal types. Due to their lack of a statically known size, these types can only exist behind some kind of pointer. Any pointer to a DST consequently becomes a fat pointer consisting of the pointer and the information that "completes" them (more on this below).

There are two major DSTs exposed by the language: trait objects, and slices.

A trait object represents some type that implements the traits it specifies. The exact original type is erased in favor of runtime reflection with a vtable containing all the information necessary to use the type. This is the information that completes a trait object: a pointer to its vtable.

A slice is simply a view into some contiguous storage -- typically an array or Vec. The information that completes a slice is just the number of elements it points to.

Structs can actually store a single DST directly as their last field, but this makes them a DST as well:

# #![allow(unused_variables)]
#fn main() {
// Can't be stored on the stack directly
struct Foo {
    info: u32,
    data: [u8],
}
#}

Rust actually allows types to be specified that occupy no space:

# #![allow(unused_variables)]
#fn main() {
struct Foo; // No fields = no size

// All fields have no size = no size
struct Baz {
    foo: Foo,
    qux: (),      // empty tuple has no size
    baz: [u8; 0], // empty array has no size
}
#}

On their own, Zero Sized Types (ZSTs) are, for obvious reasons, pretty useless. However as with many curious layout choices in Rust, their potential is realized in a generic context: Rust largely understands that any operation that produces or stores a ZST can be reduced to a no-op. First off, storing it doesn't even make sense -- it doesn't occupy any space. Also there's only one value of that type, so anything that loads it can just produce it from the aether -- which is also a no-op since it doesn't occupy any space.

One of the most extreme example's of this is Sets and Maps. Given a Map<Key, Value>, it is common to implement a Set<Key> as just a thin wrapper around Map<Key, UselessJunk>. In many languages, this would necessitate allocating space for UselessJunk and doing work to store and load UselessJunk only to discard it. Proving this unnecessary would be a difficult analysis for the compiler.

However in Rust, we can just say that Set<Key> = Map<Key, ()>. Now Rust statically knows that every load and store is useless, and no allocation has any size. The result is that the monomorphized code is basically a custom implementation of a HashSet with none of the overhead that HashMap would have to support values.

Safe code need not worry about ZSTs, but unsafe code must be careful about the consequence of types with no size. In particular, pointer offsets are no-ops, and standard allocators (including jemalloc, the one used by default in Rust) may return nullptr when a zero-sized allocation is requested, which is indistinguishable from out of memory.

Rust also enables types to be declared that cannot even be instantiated. These types can only be talked about at the type level, and never at the value level. Empty types can be declared by specifying an enum with no variants:

# #![allow(unused_variables)]
#fn main() {
enum Void {} // No variants = EMPTY
#}

Empty types are even more marginal than ZSTs. The primary motivating example for Void types is type-level unreachability. For instance, suppose an API needs to return a Result in general, but a specific case actually is infallible. It's actually possible to communicate this at the type level by returning a Result<T, Void>. Consumers of the API can confidently unwrap such a Result knowing that it's statically impossible for this value to be an Err, as this would require providing a value of type Void.

In principle, Rust can do some interesting analyses and optimizations based on this fact. For instance, Result<T, Void> could be represented as just T, because the Err case doesn't actually exist. The following could also compile:

enum Void {}

let res: Result<u32, Void> = Ok(0);

// Err doesn't exist anymore, so Ok is actually irrefutable.
let Ok(num) = res;

But neither of these tricks work today, so all Void types get you is the ability to be confident that certain situations are statically impossible.

One final subtle detail about empty types is that raw pointers to them are actually valid to construct, but dereferencing them is Undefined Behavior because that doesn't actually make sense. That is, you could model C's void * type with *const Void, but this doesn't necessarily gain anything over using e.g. *const (), which is safe to randomly dereference.