Having your IP blacklisted will severely impact your deliverability, as most ISPs and ESPs (Email Service Providers) filter emails based on blacklist records. This is why you don't want to see your name on those.
Better safe than sorry. Clean emailing activity will ensure you to stay away form blacklists.
But in case this happens, you have two different options:
Wait. Most blacklists will remove your IP from their records after few times. Depending on the degree of the offense, the duration of this process can vary, but it usually takes between 1 and 3 weeks.
Ask for removal. Some blacklists offer self-service removal or de-listing request forms on their websites. Inside your request, don't hesitate to give the context of your activity, show that you are not a spammer and ask the reasons why you got blacklisted to not make the same mistake twice.
You will find additional information about the delisting process directly on the website of the blacklist provider itself.