[Update: 10:30am (BST) systems appear to be back to normal, however if you were affected you can still contact your airlines to make claims for delayed luggage]
If you are travelling out of one of Heathrow Terminals 3 or 5, be warned that there is currently a baggage system failure and checked baggage will probably not end up at your destination. All airlines departing from these terminals are being affected.
British Airways has put out an official message on this matter, and says for those due to travel from T3 or T5:
If you plan on checking in baggage, we strongly advise you to pack essential items in your hand baggage in the event of any delay in receiving your checked bags.
Alternatively, you can change your flight to a different day, up to and including 19 June 2017. Please call us to change your flights.
If you are able to travel with hand baggage only, your travel is not affected. Hand baggage must still be within the standard allowance.
Arriving passengers should be unaffected. and if you really must travel today and your baggage does not arrive, BA will deliver it to you free of charge and reimburse any necessary purchases you make.