Although immunosuppressive treatments and target concentration intervention (TCI) have significantly contributed to the success of allogeneic haematopoietic cell transplantation (alloHCT), there is currently no consensus on the best immunosuppressive strategies. Compared with solid organ transplantation, alloHCT is unique because of the potential for bidirectional reactions (i.e. host-versus-graft and graft-versus-host). Postgraft immunosuppression typically includes a calcineurin inhibitor (cyclosporine or tacrolimus) and a short course of methotrexate after high-dose myeloablative conditioning, or a calcineurin inhibitor and mycophenolate mofetil after reduced-intensity conditioning. There are evolving roles for the antithymyocyte globulins (ATGs) and sirolimus as postgraft immunosuppression. A review of the pharmacokinetics and TCI of the main postgraft immunosuppressants is presented in this two-part review. All immunosuppressants are characterized by large intra- and interindividual pharmacokinetic variability and by narrow therapeutic indices. It is essential to understand immunosuppressants' pharmacokinetic properties and how to use them for individualized treatment incorporating TCI to improve outcomes. TCI, which is mandatory for the calcineurin inhibitors and sirolimus, has become an integral part of postgraft immunosuppression. TCI is usually based on trough concentration monitoring, but other approaches include measurement of the area under the concentration-time curve (AUC) over the dosing interval or limited sampling schedules with maximum a posteriori Bayesian personalization approaches. Interpretation of pharmacodynamic results is hindered by the prevalence of studies enrolling only a small number of patients, variability in the allogeneic graft source and variability in postgraft immunosuppression. Given the curative potential of alloHCT, the pharmacodynamics of these immunosuppressants deserves to be explored in depth. Development of sophisticated systems pharmacology models and improved TCI tools are needed to accurately evaluate patients' exposure to drugs in general and to immunosuppressants in particular. Sequential studies, first without and then with TCI, should be conducted to validate the clinical benefit of TCI in homogenous populations; randomized trials are not feasible, because there are higher-priority research questions in alloHCT. In Part I of this article, we review the alloHCT process to facilitate optimal design of pharmacokinetic and pharmacodynamics studies. We also review the pharmacokinetics and TCI of calcineurin inhibitors and methotrexate.