The presence of competing events, such as death, makes it challenging to define causal effects on recurrent outcomes. In this thesis, I formalize causal inference for recurrent events, with and without competing events. I define several causal estimands and discuss their identification and estimation under commonly arising data structures, such as randomized controlled trials. Additionally, I propose a new causal estimand, the challenge effect, to quantify the waning of vaccine protection over time. The challenge effect is identified in conventional vaccine trials, even if exposure status is unmeasured. In Chapter 1, I define a number of causal estimands for recurrent outcomes in the presence of competing events, and discuss their relation to the causal mediation literature. In particular, the separable effects are actionable contrasts of modified treatments, which disentangle treatment effects on the recurrent and competing events. Unlike previous estimands for recurrent events, the separable effects do not rely on contrasts of cross-world quantities or interventions to prevent death. I apply the results of Chapter 1 to critique a recent proposal on causal estimands in Chapter 2. In Chapter 3, I formulate a causal estimand that quantifies the average effect of treatment-switching on subsequent recurrent events. Using the assumption of no carry-over effects, I derive sharp bounds on the estimand in settings where no, or few, individuals are observed to switch between treatment arms. The bounds are used to define dynamic treatment regimes based on decision theory for partially identified treatment effects. Finally, in Chapter 4, I define the challenge effect, which quantifies vaccine waning in terms of infection-related events. The challenge effect can be understood intuitively by reference to a target trial where participants are challenged with the infectious agent after vaccination. Plausible, non-parametric assumptions are used to identify sharp bounds on the challenge effect. The approach is illustrated by estimating bounds on the waning of the BNT162b2 COVID-19 vaccine using publicly available summary data from a vaccine trial.