The . operator in Rust comes with a lot of magic! When you use ., the compiler will insert as many *s (dereferencing operations) necessary to find the method down the deref "tree". As this happens at compile time, there is no runtime cost of finding the method.

let mut name: String = "hello world".to_string();
// no deref happens here because push is defined in String itself
name.push('!');

let name_ref: &String = &name;
// Auto deref happens here to get to the String. See below
let name_len = name_ref.len();
// You can think of this as syntactic sugar for the following line:
let name_len2 = (*name_ref).len();

// Because of how the deref rules work,
// you can have an arbitrary number of references. 
// The . operator is clever enough to know what to do.
let name_len3 = (&&&&&&&&&&&&name).len();
assert_eq!(name_len3, name_len);

Auto dereferencing also works for any type implementing std::ops::Deref trait.

let vec = vec![1, 2, 3];
let iterator = vec.iter();

Here, iter is not a method of Vec<T>, but a method of [T]. It works because Vec<T> implements Deref with Target=[T] which lets Vec<T> turn into [T] when dereferenced by the * operator (which the compiler may insert during a .).

Given two types T and U, &T will coerce (implicitly convert) to &U if and only if T implements Deref<Target=U>

This allows us to do things like this:

fn foo(a: &[i32]) {
    // code
}

fn bar(s: &str) {
    // code
}

let v = vec![1, 2, 3];
foo(&v); // &Vec<i32> coerces into &[i32] because Vec<T> impls Deref<Target=[T]>

let s = "Hello world".to_string();
let rc = Rc::new(s);
// This works because Rc<T> impls Deref<Target=T> ∴ &Rc<String> coerces into 
// &String which coerces into &str. This happens as much as needed at compile time.
bar(&rc); 

For functions that need to take a collection of objects, slices are usually a good choice:

fn work_on_bytes(slice: &[u8]) {}

Because Vec<T> and arrays [T; N] implement Deref<Target=[T]>, they can be easily coerced to a slice:

let vec = Vec::new();
work_on_bytes(&vec);

let arr = [0; 10];
work_on_bytes(&arr);

let slice = &[1,2,3];
work_on_bytes(slice); // Note lack of &, since it doesn't need coercing

However, instead of explicitly requiring a slice, the function can be made to accept any type that can be used as a slice:

fn work_on_bytes<T: AsRef<[u8]>>(input: T) {
    let slice = input.as_ref();
}

In this example the function work_on_bytes will take any type T that implements as_ref(), which returns a reference to [u8].

work_on_bytes(vec);
work_on_bytes(arr);
work_on_bytes(slice);
work_on_bytes("strings work too!");

use std::ops::Deref;
use std::fmt::Debug;

#[derive(Debug)]
struct RichOption<T>(Option<T>); // wrapper struct

impl<T> Deref for RichOption<T> {
    type Target = Option<T>; // Our wrapper struct will coerce into Option
    fn deref(&self) -> &Option<T> {
        &self.0 // We just extract the inner element
    }
}

impl<T: Debug> RichOption<T> {
    fn print_inner(&self) {
        println!("{:?}", self.0)
    }
}

fn main() {
    let x = RichOption(Some(1)); 
    println!("{:?}",x.map(|x| x + 1)); // Now we can use Option's methods...
    fn_that_takes_option(&x); // pass it to functions that take Option...
    x.print_inner() // and use it's own methods to extend Option
}

fn fn_that_takes_option<T : std::fmt::Debug>(x: &Option<T>) {
    println!("{:?}", x)
}

Deref has a simple rule: if you have a type T and it implements Deref<Target=F>, then &T coerces to &F, compiler will repeat this as many times as needed to get F, for example:

fn f(x: &str) -> &str { x }
fn main() {
    // Compiler will coerce &&&&&&&str to &str and then pass it to our function
    f(&&&&&&&"It's a string"); 
}

Deref coercion is especially useful when working with pointer types, like Box or Arc, for example:

fn main() {
    let val = Box::new(vec![1,2,3]);
    // Now, thanks to Deref, we still 
    // can use our vector method as if there wasn't any Box
    val.iter().fold(0, |acc, &x| acc + x ); // 6
    // We pass our Box to the function that takes Vec,
    // Box<Vec> coerces to Vec
    f(&val)
}

fn f(x: &Vec<i32>) {
    println!("{:?}", x) // [1,2,3]
}