In response to BryceM, above; I have only shot one buffalo, so I can hardly claim to be an expert, for which I was using a double rifle in .470.
The first shot was broadside at about 65 yards, right on the shoulder. The bullet (a Rhino solid) unfortunately fragmented, and what was left of it deflected into the brisket. By the time that I was back on target, the buffalo (and his two askaris) was making a quick getaway and an - in any way proper - follow-up shot was impossible before they all disappeared into the mopani bush.
Follow-up. The classic 'P-turn' and ambush from the side. The PH saw him in good time and fired, grazing the buffalo's cheek, at which point the buffalo turned tail again.
Four hours after the first shot, he charged the PH, running in front of me right to left at approximately 25 yards. The first shot was just behind the heart, in the lungs - not, of course, that that had any immediate effect; the second (I freely admit, a badly-placed flyer) broke his spine just in front of the hips. That, however, was enough to break the charge, and he came down 8 yards from the PH (who, in the meantime, having fired himself, had taken a step backwards, tripped and was sitting on his bum). The benefits of having a double rifle.
My own takeaways from the experience are, firstly, that Mr. Murphy's law holds good; and, secondly, that in that final charge - which happens very quickly - it is imperative both to (try to) place your shots and stitch the air with lead: but these requirements are, by their nature, contradictory. But, as I say, I am no expert.
This, incidentally, took place at the Mabalabala game ranch in the Limpopo. For all the criticism of such establishments - not from me - the experience was authentic enough for my taste.