In the last decade, fungal respiratory diseases have been increasingly investigated for their impact on the clinical course of people with cystic fibrosis (CF), with a particular focus on infections caused by Aspergillus spp. The most common organisms from this genus detected from respiratory cultures are Aspergillus fumigatus and Aspergillus terreus, followed by Aspergillus flavus, Aspergillus niger, and Aspergillus nidulans. These species have been identified to be both chronic colonizers and sources of active infection and may negatively impact lung function in people with CF. This review article discusses definitions of aspergillosis, challenges in clinical practice, and current literature available for laboratory findings, clinical diagnosis, and treatment options for pulmonary diseases caused by Aspergillus spp. in people with CF.