The overall aim of this thesis is to improve knowledge about the prevention of infectious and bleeding complications in patients with hematological malignancies, primarily in those with chronic lymphocytic leukemia (CLL) and myelodysplatic syndrome (MDS). Hypogammaglobulinemia, impaired production of immunoglobulins (Ig), is an established risk factor for infection, but the impact of IgG pure subclass deficiency (IgG subclass deficiency with adequate production of IgG, IgA, and IgM) has been debated. In a retrospective single institution study, we concluded that pure IgG subclass deficiency in CLL patients is rare and is not associated with an increased risk of infection. Hence, routine analysis of IgG subclasses in patients with CLL is not warranted. There is no consensus on recommending vaccination against Streptococcus pneumoniae to CLL patients mainly because comparative studies are lacking. In our randomized trial, the efficacy of a conjugated pneumococcal vaccine on immune response was superior or equal to a polysaccharide vaccine for all pneumococcal serotypes common for the two vaccines. A conjugate pneumococcal vaccine should therefore be included in vaccination programs for patients with CLL. Bronchoalveolar lavage (BAL) is a well-established invasive method to identify the cause of pulmonary infiltrates in immunocompromised patients. In a retrospective trial, we have studied the diagnostic yield of BAL in patients with hematological malignancies. We concluded that BAL is highly useful in either verifying or excluding some of the important respiratory tract infections affecting these patients, particularly invasive pulmonary aspergillosis (IPA) and Pneumocystis jirovecii pneumonia (PJP). However, standardized procedures for BAL sampling should be continually revised to avoid unnecessary microbiological tests. Thrombocytopenia, an adverse prognostic factor in patients with MDS, can be aggravated by azacitidine, first-line treatment for high-risk MDS. Eltrombopag, a thrombopoietin-receptor agonist (TPO-R), alleviates thrombocytopenia in patients with immune thrombocytopenic purpura (ITP). In a phase I clinical trial, we concluded that the combination of eltrombopag and azacitidine in high-risk MDS patients with thrombocytopenia is feasible and well tolerated in doses up to 200 mg eltrombopag daily.