Ceiling soundproofing can often be the only option for people suffering with noisy neighbours living above them. There are two main options:
1. Is to remove the existing ceiling and soundproof it this way by using materials in between the joists and use a resilient channel system. This creates isolation from the floor above meaning the sound that's being transferred isn't coming directly through the floor above and onto the ceiling below as the bars create isolation.
2. This option involves leaving the existing ceiling in place and creating a new one below it using new timbers etc. This isn't always possible as it takes up 7-8 inches of room height so people with lower ceilings would always go for the first option. A new ceiling here is created giving complete isolation from above so would generally work better if a little more space can be lost. (This would be recommended for high impact noise problems).
If there is just a problem with airborne sound transference like speech or TV noise then it can often be a more simple job with materials being added to the existing ceiling.