Require, Import, Require Import

In Coq, what's the difference between ... ?

Require X.
Import X.
Require Import X.

I have basically memorized some common patterns. I usually see code using Require Import X. Then there's Import ListNotation. And I just noticed it's also possible to write just Require X. What's the difference? Some practical examples would be appreciated.

Require loads a library whereas Import brings its definitions into scope. Require Import does both. If you only have the library loaded, you'll need to refer to names fully qualified. Coq allows top-level modules corresponding to files to define modules; these have to be imported separately to bring all of their definitions into scope, and they can't be Required - that's what's going on with ListNotations:

(* List is not loaded by default *)
Fail Check List.map.

(* the full name is technically Coq.Lists.List *)
Require List.

(* note that lists are actually defined in Coq.Init.Datatypes which is 
imported by default, so [list] is  unqualified and the [x::xs] notation is 
already defined *)
Print List.map.
(*
List.map =
fun (A B : Type) (f : A -> B) =>
fix map (l : list A) : list B :=
  match l with
  | nil => nil
  | (a :: t)%list => (f a :: map t)%list
  end
    : forall A B : Type, (A -> B) -> list A -> list B
*)

(* bring everything in List into scope *)
Import List.
(* this includes the ListNotations submodule *)
Import ListNotations.

(* note that now list notations are available, and the list notation scope is
open (from importing List) *)
Print List.map.
(*
map =
fun (A B : Type) (f : A -> B) =>
fix map (l : list A) : list B :=
  match l with
  | [] => []
  | a :: t => f a :: map t
  end
    : forall A B : Type, (A -> B) -> list A -> list B
*)

Note there are some quirks with how Coq handles modules, especially compared to other languages:

Coq does not require a full path to a module, only an unambiguous suffix. Indeed I rarely see full import paths, even to standard library modules.
Notations cannot be used except by importing the module, and unlike most objects there's no way to refer to a notation, fully qualified or otherwise.
Importing a module can have side effects, for example changing notation interpretation scopes or setting options if you use Global Set in the module being imported.
Importing is fairly limited (especially compared to Haskell) - there's no way to rename a module at import time, or selectively import some definitions.