Invasive fungal diseases (IFDs) still represent a relevant cause of mortality in patients affected by hematological malignancies, especially acute myeloid leukaemia (AML) and myelodysplastic syndrome (MDS) undergoing remission induction chemotherapy, and in allogeneic hematopoietic stem cell transplantation (allo-HSCT) recipients. Mold-active antifungal prophylaxis (MAP) has been established as a standard of care. However, breakthrough IFDs (b-IFDs) have emerged as a significant issue, particularly invasive aspergillosis and non-Aspergillus invasive mold diseases. Here, we perform a narrative review, discussing the major advances of the last decade on prophylaxis, the diagnosis of and the treatment of IFDs in patients with high-risk neutropenic fever undergoing remission induction chemotherapy for AML/MDS and allo-HSCT. Then, we present our single-center retrospective experience on b-IFDs in 184 AML/MDS patients undergoing high-dose chemotherapy while receiving posaconazole (n = 153 induction treatments, n = 126 consolidation treatments, n = 60 salvage treatments). Six cases of probable/proven b-IFDs were recorded in six patients, with an overall incidence rate of 1.7% (6/339), which is in line with the literature focused on MAP with azoles. The incidence rates (IRs) of b-IFDs (95% confidence interval (95% CI), per 100 person years follow-up (PYFU)) were 5.04 (0.47, 14.45) in induction (n = 2), 3.25 (0.0013, 12.76) in consolidation (n = 1) and 18.38 (3.46, 45.06) in salvage chemotherapy (n = 3). Finally, we highlight the current challenges in the field of b-IFDs; these include the improvement of diagnoses, the expanding treatment landscape of AML with molecular targeted drugs (and related drug–drug interactions with azoles), evolving transplantation techniques (and their related impacts on IFDs’ risk stratification), and new antifungals and their features (rezafungin and olorofim).