Recently, movable antenna (MA) has attracted wide attention in wireless communications due to its potential in enhancing wireless communication performance via local movement within a confined region. However, antenna position optimization (APO) has emerged as a major challenge for MAs, due to the lack of a tractable, analytical, and accurate channel model in terms of antenna positions. Although existing works have developed various algorithms for APO, most of them are based on simplified theoretical channel models, which limit their generality. To address this challenge, in this article, we present more general and effective APO algorithms for different purposes, categorized as continuous APO and discrete APO, respectively. Continuous APO is mainly applied for flexible array signal processing to boost large-scale communication performance, while discrete APO is applied for small-scale multi-path channel reshaping. Specifically, the discrete APO discretizes the antenna movement region into multiple sampling points and employs discrete algorithms to determine the optimal MA positions based on the point-wise channel state information (CSI), without the need for an analytical channel model. To reduce the overhead for CSI acquisition, we also present more efficient learning-based APO algorithms that operate without requiring full point-wise CSI. Finally, we compare the application scenarios of the proposed algorithms and validate their effectiveness with numerical results.