Organ transplantation is a treatment option for severe disease. Understanding its impact on survival relies on observational data such as national transplant registers, as randomized trials are infeasible. In this work we specify target trials to articulate different causal questions and discuss how to answer them using longitudinal data on patient measures, transplant status, and survival. The motivation is a study of the impact of lung transplantation on survival in cystic fibrosis. Causal questions include what the effect is of joining the transplant wait-list and what the effect of transplant is in those who received one. We consider both population-average and personalised effects. Different approaches to addressing time-dependent confounding and estimating the causal quantities of interest and will be discussed. These include methods based on forming a sequence of emulated trials within the longitudinal data and using inverse probability weighting in the estimation, and g-estimation. Organs are a finite resource and organ allocation depends on a match between certain donor and recipient characteristics. I will discuss the challenges this brings and how they can be addressed.