This thesis studies asymptotic dynamics of the classical Lotka-Volterra competition model of two populations when one of the populations is subject to Allee effects. The model can have either no interior steady state, a unique interior steady state or two interior steady states. Using the tools of monotone systems, we provide global asymptotic dynamics of the model and determine competition outcomes. We derive sufficient conditions for which the model either has one, two or no interior steady states. We then incorporate stocking into the population with Allee effects important for studies of population conservation. We analyze the resulting model and provide global dynamics of the system to study the impact of stocking upon population interaction.