Memristors are among the most promising devices for building neural processors and non-volatile memory. One circuit design stage involves modeling, which includes the option of memristor models. The most common approach is the use of compact models, the accuracy of which is often determined by the accuracy of their parameter extraction from experiment results. In this paper, a review of existing extraction methods was performed and new parameter extraction algorithms for an adaptive compact model were proposed. The effectiveness of the developed methods was confirmed for the volt-ampere characteristic of a memristor with a vertical structure: TiN/HfxAl1−xOy/HfO2/TiN.