Fishing is one of the earliest occupation in the planet, and it represents the backbone of many countries' economy. Carrying capacity is an important concept in ecology because it represents population's growth limit; however in the literature it is always considered to be constant, which is not a realistic assumption because it might change (increase and/or decrease) according to environmental and artificial reasons. In this thesis, several mathematical models were developed for fishery population growth assuming different growth functions with variable carrying capacity considering different harvesting strategies. All these models were fully mathematically analysed and numerically simulated to understand their dynamics. In order to determine the optimum harvesting strategy in each one of the cases, the maximum sustainable yield was calculated; also optimal control problems were developed and solved.