Most responses here are totally out of touch and do not cater for the majority of kids actually being bullied. When you are one of the smallest kids in the year, and it's several of them picking on you, do you think these victims have the confidence to stand and smack one of them? No they don't. Get real. You can tell your kids to fight back all you want, but most won't, because they are scared and are nice people that don't want to hurt others. You can explain that the bullies deserve it and it's ok to stand up for yourself all you like but they are not in a place where they can confidently physically stand up to them.
A lot of the bullying is very, very subtle targeted abuse verbally/mentally as well. It builds up over time. It's the tiny little comments in class deliberately crafted to wind up the victim, over, and over again. Subtle exclusions from group activities, or minor things that all add up to making the victim have a harder life. Many of it is via social media or on xbox live/ps4/game chat as well. Bullies have become conditioned now to know that they can tell on the actual victim, the moment they do anything back. The bullies group together and play the game too. It's all well and good recommending martial arts and the likes, but not all kids take to the formal discipline side of it very well and it can be very boring and lack fun imo, compared to a lot of other sports.
Some teachers are completely unaware of what goes on in the playground and out of their earshot. When you go to try to bring this up with the school, they aim to "take it seriously" and address it but this can make it worse. The parents if approached go into self preservation mode and stand up for their child too. I've even seen good friends turn on each other when it suits their outlook of what was or was not done.
It's a massively complex thing with no clear answer. If you can encourage your child to physically fight back, that's great. But this presents it's own problems in that often the victim then gets grassed up for smashing Jonny's nose in and is punished. This can then cause them to never want to fight back again since such a big thing gets made of their "awful actionos", and they don't understand why people don't see their (correct) side. It can be very hard to sort out for teachers as well.
With regard to the op then if it's mainly school that is the issue, whilst it can sound drastic, a change of school can work wonders. I've been through this myself and it's the best decision I ever made for my kid. I've encouraged mine to also smack the bully but they've never been able to, and that is absolutely no fault of them or I.
Speak to the school. Speaking to parents works less well....most don't take it seriously if it's not their own kid being bullied. I've seen this first hand with "friends" that play it down as "boys will be boys" and "girls will be girls" and "it's just banter" attitudes. They tend to try to laugh it off or claim that their child said that your child also does stuff to them too bla bla bla. When you get tough with the parent, it tends to turn into a tough stance back that their child is amazing and wouldn't do this kind of stuff. Extra points for them then posting about it on facebook that you're crazy and calling their kid a bully. I've seen it all honestly.
I've dealt first hand with resolving bullying of young children having ran a football team. Won't go into detail but it's a constant battle and requires a no tolerance policy and be prepared to ban even your best players if it happens.