Successful prospective memory (PM) involves not only detecting that an environmental cue requires action (i.e., prospective component), but also retrieval of what is supposed to be done at the appropriate moment (i.e., retrospective component). The current study examined the role of attention and memory during PM tasks that placed distinct demands on detection and retrieval processes. Using a large-scale individual differences design, participants completed three PM tasks that placed high demands on detection (but low demands on retrieval) and three tasks that placed high demands on retrieval (but low demands on detection). Additionally, participants completed three attention control, retrospective memory, and working memory tasks. Latent variable structural equation modeling showed that the prospective and retrospective components of PM were jointly influenced by multiple cognitive abilities. Critically, attention and retrospective memory fully mediated the relation between working memory and prospective memory. Furthermore, only attention uniquely predicted PM detection, whereas only retrospective memory uniquely predicted PM retrieval. These findings highlight the value of independently assessing different PM components and suggest that both attention and memory abilities must be considered to fully understand the dynamic processes underlying prospective remembering.