In the 21st century, with social life changing, we have to make an effort to catch up with our studies. By this I mean we need to do homework, which the teachers always pile on us. There are many different opinions about the benefits of homework. In my opinion, there are both advantages and disadvantages.
[I'm not sure what you mean by "study to catch up this modern life" so I've put something which is correct but might not be what you have in mind.
There is no verb in sentence three. Every sentence must contain a verb.
You can say something is controversial, or you can say there different opinions about it, but you can't say there are different controversies.]
The main advantage of doing homework is that it helps us to remember the information taught to us in the class. In addition, by seeing our written work, our teachers find out what we learnt and understood. From this, they might change their method of teaching to make it easier to understand their lessons. Moreover, doing a lot of homework may provide some necessary knowledge to make it easier for us to find a good job in the future.
[There was quite a bit of repetition in this so I've just tidied it up a bit]
On the other hand, there are several disadvantages to homework. It can cause especial stress, which is harmful in our lives. Having to stuff many facts into our brains through excessive homework may not only useless to us, but may also get us stressed very easily. Moreover, it may have bad effect on our health [such as wearing glasses of students, even little kids.]
[If a sentence starts "Besides that," it means that what follows agrees with what we have just put. But here, you are writing the opposite, the disadvantages, so "On the other hand" is better.
"Knowledge" is always singular. I suggest "facts".
I would avoid the part about wearing glasses, if you are saying that reading leads to having to bad eyesight -- it doesn't. At worst, it might cause headaches. Perhaps instead: "It may have a bad effect on our health, such as headaches caused by having to work too late into the night."
It is "effect" when a noun -- as here -- and "affect" when a verb. e.g. "It had a bad effect on my health", but "My health was badly affected by it."]
To sum up, doing homework is very important to review our knowledge but we must not overuse it and force our children to do it all day. [?Nothing is perfect.] Therefore, we have to find the right balance between doing homework and relaxing through outside activities and such-like.
[I'm not sure what you mean by "Nothing is perfect" here.]