Brickwork Cracks

In the drought that most of Australia is in the grip of at the moment, I wouldnt try to fix any cracks in brickwork just yet, I would wait until the weather returns to normal conditions, then see what the brickwork is doing.
The ground may swell back to its original position again.

Foundation Failure.
Cracks in brickwork are due mainly to foundation failure, which can be caused by the ground drying out, or subsiding.
Bad site preperation is another cause for foundation failure.

Below is a typical example of foundation failure.

You can try to patch up the crack in the brickwork, but in most cases you will be wasting your time.
If the crack has appeared because the ground has dried out, once the ground gets wet again it will try to get back to where it used to be.
If you have bogged up the crack with mortar in the attempt to fix it and the ground swells again due to moisture, you will find that the extra mortar in the joint will actually push the brickwork above the crack upwards.

The best remedy is to take out the brickwork and re-do it, assuming of course that you address the underlying cause of foundation failure.

The other main cause of brickwork failure is impact to the brickwork, once again it it best to pull down the brickwork and re-do it from the start.

Tree roots can also cause brickwork failure, Im not sure if its from the force of the roots, or the effect of the roots drying out the surrounding soil.
I have a feeling it's from the drying effect of the roots.
But the remedy is the same in that you will have to re-do the brickwork and rectify the cause.

Patching brickwork is rarely successful, unless it is just for a brick or two.

Expansion Joints, or Control Joints can stop brickwork from cracking as they allow the brickwork some movement, but it wont eliminate cracking entirely.

I form the expansion joinst using a 12mm diameter steel rod, the rod is easy to remove from the brickwork prior to finishing off the wall.

The gap left by the rod is filled with a strip of foam and then caulked up after the works have finished.