My DS is 17mo and started tantruming around 14mo. It's either 'inexplicable' or some minor misdemeanor of mine, such as not letting him pick up dog poo, which sets him off. However, whatsoever the source of the outburst, I tend to assume that his experience of total-body, all-consuming rage is genuine so respond with sympathy - basically I 'contain' him til it's over and comfort him when he's coming out of it. I try to speak to him in a way that shows him I understand and feel sympathy for his feelings (which in no way means he can pick up the poo, as it were).
It's probably an age thing (rather than because of my 'interventions') but the tantrums are definitely less potentially self-destructive - he hasn't tried to throw himself out of my arms for ages, for example, - and I think it's probably a combination of my being practiced and him continuing to grow, but he rarely has hurt me with biting/ etc. (though he did today - I used my standard line 'Even if you are very cross with mummy, you mustn't bite')
I don't want to put him down or sanction him because I don't want him to think his overwhelmingly difficult emotions will make me walk away from him. I want him to know that there is nothing about him so terrible it can push me away. I also think two of us getting het up is hardly going to help the situation, so I try not to panic, or show him I feel out of control or worried - I just try to let him know I'm concerned for him but not about the situation.
I think tantrums are (a) par for the course (b) not within the child's capacity to prevent or stop and (c) horrifying most of all for the tantrumer (yes, even when he's chosen to do it in a supermarket isle just as MIL comes round the corner). So with that in mind, I tend not to try to react too much or take it as a reflection on my parenting, but do try and help him get through it with minimal fuss. That's what I'd recommend, really, - trust your child is going through an appropriate stage; know that a care giver who works to calm him will teach him to calm himself; keep him safe and loved while he goes through this stage which must be terrifying for him; remember it's developmental and not personal; remember that all children want to be like the adults they love and so don't want to use tantrums etc. to get their needs met.
Otherwise, I can really recommend a constant drip-feed of raisins, apples, toast fingers, yoghurt, nutty bars, strawberries etc. because a little bit hungry = really quite mardy in our house. And distraction BEFORE the event. If it can be predicted...