Internal organ transplantation is a high-tech medical intervention that significantly improves patient survival and quality of life. However, infections remain the leading cause of mortality in organ transplant recipients. Invasive aspergillosis (IA) is the second most common invasive fungal infection in this population and is associated with high mortality rates, reaching up to 90%. This article presents a clinical case of IA following heart transplantation (HT), along with an analysis of registry data and institutional experience in managing this serious complication based on registry data. Between September 2010 and October 2024, 23 adult patients with IA following an internal organ transplantation were included in the institutional registry. Most IA cases occurred after heart transplantation (65%), followed by kidney transplantation (31%), and, less commonly, lung transplantation (4%). The lungs were the primary site of IA (96% of cases). Diagnosis was confirmed through direct microscopy of clinical samples, such as bronchoalveolar lavage (BAL) fluid and tissue biopsies, in 50% of patients, while fungal cultures yielded positive results in 35% of cases. The predominant pathogen was Aspergillus fumigatus (73%), followed by Aspergillus niger (18%) and Aspergillus flavus (9%). A positive galactomannan test in BAL was detected in 85% of patients. All patients received targeted antifungal therapy, primarily with voriconazole (87%), while echinocandins and itraconazole were used in 17% and 4% of cases, respectively. Overall 90-day patient survival was 78%. The literature review outlines the main approaches to the diagnosis and management of invasive infections associated with Aspergillus spp.