Predation is one of the basic mechanisms of population growth control. Using a mathematical model, we explore the impact of predation in a prey population structured into two age classes, juveniles and adults, assuming a generalist predator. The specific predation pressure is represented for each of the two age classes by either no predation or Holling type II or Holling type III functional responses in various combinations. We distinguish two scenarios. In the first one, we seek for potential Allee effects or multiple stable states in the prey population, and explore the conditions at which the predation is more effective on juveniles than adults and vice versa. The most interesting finding here is the occurrence of bistability, or a predator-pit-like behaviour, when predators consume only juvenile prey, via a Holling type II functional response, an observation not described previously. In case only adults or both age classes are killed by predators exhibiting a type II functional response, the Allee effect occurs frequently. Multiple positive stable states are commonly observed if one of the age classes is exploited via a type III functional response. In the second scenario, we assume that the prey feeds on a resource and that the resource together with the prey undergoes outbreak dynamics, and we examine possibilities of control of such outbreaks using age-specific predation. Predation was proven to be able to suppress the prey population successfully. In some cases, an oscillation-free resource-prey-predator coexistence was detected.