XYZ is a convention whereby the first 3 bids of a partnership's auction are on the 1-level (but not 1NT- over 1NT you can play some version of Responder's bid in a new minor after opener's notrump rebid to check for major suits New Minor Forcing). SO, it goes 1-something, 1-something, then 1-of-a-major. After those 3 bids (1X-1Y-1Z), the typical treatment is to use:

2 by responder as an When a suit is bid but says nothing about the holding in that suit artificial relay. Opener must bid 2.

2 by responder as an When a suit is bid but says nothing about the holding in that suit artificial bid, saying that the partnership is going to at least game.
Other bids by responder are natural and NOT Forcing; 2-level suit bids are typically weak, 2NT and 3-level bids are invitational.

Responder's 2 relay is used to either place the contract in 2, or to be followed by an invitational bid.

Examples below:

A]
1-1
1:

The responder can bid 2 to force opener to bid 2. After this, responder can pass to play there, or make an invitational bid (such as 2, which would promise at least 5 hearts). Responder can also bid 2 to set up a Game Force.
Other actions as above.

B]
1-1
1:

Nothing changes. Responder can relay with 2 or start a Game Force with 2. In both cases, of course, the 2-of-a-minor bid is completely artificial. 1 here would be natural and forcing (but NOT game forcing).

If using XYZ, it does not matter what the first 3 bids were, as long as opener's rebid is 1 or 1.

Of course, the major downside (other than forgetting) is that the partnership can't play in a 2 contract after a 1 opening.

As with any convention, the partnership must decide if this is on in competition (I recommend NO) or by a Passed Hand (I recommend NO).

This treatment has been steadily gaining in popularity since the turn of the millennium.