They knew there would be trouble unless the report was finished by the next day.

would 是 will 的过去式形式，在这里表示"将会"，用于表达过去时间点对未来情况的推测或预期。 unless 是一个连词，意思是"除非"，用于引出某种条件，表示如果不满足这个条件，就会发生主句所述的情况。