Eight year olds typically value friendships greatly and now more than ever will see them as increasingly important. Around this age children typically identify a ‘best' friend - this is an important developmental milestone.
However, along with this development will inevitably come the trials and tribulations of having a ‘best' friend. Squabbles and fall outs are natural, but may hit your child much harder than they have done previously. Conversely, if your child hasn't identified a ‘best' friend yet, this can leave them somewhat at sea: school can be a lonely place if you're not part of a pair.
How should you handle it?
To make matters all the more tricky, your child is now self-aware enough to mask their emotions. As they grow, they will be increasingly inclined to try to solve situations/problems for themselves. As such, keeping lines of communication open is key now. It's only right that your child wants to learn to deal with things by themselves (and is indeed a key part of their development); however if you are concerned about your child's friendships you'll need to pay close attention to your child, as they may not automatically turn to you for help now.
Make sure that you're still setting aside a little time each day to talk to your child about school, their friends and so on. If you are concerned that something might be wrong, then encourage them to confide in you.
If they're feeling a little lonely because everyone else seems to have a best friend but they don't, be supportive of their feelings and acknowledge that at times these things can be difficult. If possible, help them to build up closer friendships by encouraging them to invite other children over after school. Or, if they have particular interests or hobbies - sport, music, art etc - encourage them to go to after school clubs where they can meet other like-minded children who enjoy similar activities.
If they do fall out with their friends, don't dismiss it as a childhood squabble. Instead offer sympathy and support. Take the time to explain that from time to time friends do fall out with each other, but it doesn't necessarily mean that they won't ever be friends again. Encourage them to talk through what happened and discuss ways that they might look to resolve the situation.