If services rendered and expenses incurred happen in 2018 but compensation for services don't occur until 2019, how is that handled?

[dr5]

Assuming that you are asking this question as an individual, you are a Cash Basis taxpayer.  Income is taxable to you in the year that you receive the money.  Note that if you are received funds in 2019, the payer should also furnish you with a 1099 for 2019 in 2020.