The successful management of biological populations is essential to both the world's economic and environmental wellbeing. This includes controlling invasive species and sustainably harvesting biological resources for profit. In the first chapter we consider monitoring programs for the management of invasive populations that we wish to eradicate. Previous theoretical studies have argued that managers are allocating too much effort to programs for determining the location of invasive species in a managed area. In contrast, managers view early detection as the key to invasive species management. Intuitively, the importance of early detection makes sense because early detection can lead to early intervention and therefore massive ecological and economic benefits. In this chapter we provide a theoretical explanation for why it is optimal to deploy an intense initial search for the invader and why past studies have underestimated optimal surveillance effort. In the second chapter we consider populations that are harvested for profit. Due to high economic and ecological stakes in determining sustainable harvest policies for renewable resources, such as timber, fish and game, optimal harvest is a widely studied problem in bioeconomics. However, most of the work focuses on simple models for the harvest of unstructured populations, even though demographically structured population models are more commonly used for population assessment. In this chapter we derive optimal escapement rules for both deterministic and stochastic stage-structured population models. When considering environmental stochasticity, optimal harvest of the pre-reproductive life stage is either more aggressive or more conservative than in the deterministic case, depending on the second and third derivative of the recruitment function. However, when harvesting reproductive adults, optimal harvest is the same as in the deterministic case. In the third chapter we ask "how much do these optimal management plans, generated using simplified models, perform when a population is more complex?" Can a manager use their expert judgment and flexibility to outperform simple models that make incorrect assumptions about population dynamics? As a first step towards answering this question, we conducted experiments where human subjects managed a hypothetical simulated population, by playing an online game, and compared their performance to the performance of decisions developed by mathematical models. The models, on average, outperformed human judgment, even when they made incorrect assumptions about the simulated population's dynamics. However, in some scenarios the models produced undesirable results. Therefore, we recommend that managers use mathematical models as a supplement, rather than a replacement, for expert judgment.