OR queries in Firebase

Firebase currently can only query on a single child property. So if you want to query multiple properties, you'll have to combine them into one:

Messages
  -DFHJ3498ua
    from: Tony
    to: Bob
    from_to: Tony_Bob
    message: "Hello Bob, this is Tony"
  -DFHJ3598uz
    from: Bob
    to: Tony
    from_to: Bob_Tony
    message: "Hello Tony, What can I do for you?"
  -EFHJ3498ua
    from: Tony
    to: Bob
    from_to: Tony_Bob
    message: "Can you help me with this Firebase query?"

You can then query for messages from Bob to Tony using:

var ref = new Firebase('https://your.firebaseio.com/Messages');
var query = ref.orderByChild('from_to').equalTo('Bob_Tony');
query.on('value', function(snapshot) {
  console.log(snapshot.val()); // all messages from Bob to Tony
});

In a chat-like application, you might want to consider actually using the sender-receiver pair as the key:

Messages
  from_Bob_to_Tony
    -DFHJ3598uz
      from: Bob
      to: Tony
      message: "Hello Tony, What can I do for you?"
  from_Tony_to_Bob
    -DFHJ3498ua
      from: Tony
      to: Bob
      message: "Hello Bob, this is Tony"
    -EFHJ3498ua
      from: Tony
      to: Bob
      message: "Can you help me with this Firebase query?"

With this data structure you won't have to run a query to get the relevant messages, but can do a direct lookup.

var ref = new Firebase('https://your.firebaseio.com/Messages');
var query = ref.child('from_Bob_to_Tony');
query.on('value', function(snapshot) {
  console.log(snapshot.val()); // all messages from Bob to Tony
});