Inclusion Criteria:  Patients are eligible for inclusion if all of the following criteria are met:  Age ≥ 18 years Planned to undergo alloSCT for one of the following haematological malignancies: acute leukaemia (including myeloid and/or lymphoid lineage or biphenotypic), myelodysplastic syndrome, chronic lymphocytic leukaemia (CLL), B-cell non-Hodgkin lymphoma (NHL) and plasma cell myeloma Physician preference for a non-myeloablative conditioning regimen Available 10/10 HLA-matched related or unrelated haematopoietic stem cell donor Transplantation to be performed from a peripheral blood stem cell source  Adequate renal and hepatic function at screening as follows:  Calculated creatinine clearance >50ml/min as measured by Cockroft Gault formula AST and ALT ≤ 3.0 x ULN Bilirubin ≤ 1.5 x ULN (except patients with Gilbert's Syndrome) Able to tolerate oral medications  Disease status at the time of transplantation as follows:  Acute leukaemia in complete morphologic remission Myelodysplastic syndrome with less than 10% bone marrow blasts CLL in complete remission (CR), partial response (PR) or PR with lymphocytosis NHL in CR or PR Myeloma in CR, very good partial response (VGPR) or PR within 3 months of prior autologous stem cell transplantation as part of a tandem auto-allo transplant approach ECOG performance status 0-1  Exclusion Criteria:  Patients will be excluded from this study if any of the following criteria are met:  Moderate or high risk of tumour lysis syndrome prior to conditioning for allogeneic transplantation, defined as:  For CLL: Diameter of any lymph node or tumour mass >5cm OR absolute lymphocyte count≥25x10^9/L For NHL: Diameter of any lymph node or tumour mass >5cm  Prior intolerance of venetoclax or another BCL-2 inhibitor with the exception of cytopenias. Patients with prior clinical tumour lysis syndrome following venetoclax or other BCL-2 inhibitor will be excluded from the study if at the time of prior TLS their disease burden was as follows:  For CLL: Diameter of any lymph node or tumour mass <5cm OR absolute lymphocyte count≤25x10^9/L For NHL: Diameter of any lymph node or tumour mass <5cm Reticulin fibrosis of the marrow of grade MF 2-3 Prior allogeneic stem cell transplantation Haemopoietic cell transplantation - comorbidity index (HCT-CI) score > 5 Any currently active malignancy other than the primary indication for alloSCT (except localized basal cell carcinoma or squamous cell carcinoma of the skin) Uncontrolled systemic infection Known malabsorption syndrome Has received within 7 days prior to the first dose of venetoclax CYP3A4 inducers such as rifampicin, carbamazepine, phenytoin and St John's wort Has received within 7 days prior to the first dose of venetoclax CYP3A4 inhibitors Known positivity to HIV Significant physical or psychiatric comorbid illness that in the investigator's opinion would impair the patient's ability to participate in the study.