To enable next-generation wireless communication networks with modest spectrum availability, multiple-input multiple-output (MIMO) technology needs to undergo further evolution. In this paper, we introduce a promising next-generation wireless communication concept: flexible MIMO technology. This technology represents a MIMO technology with flexible physical configurations and integrated applications. We categorize twelve representative flexible MIMO technologies into three major classifications: flexible deployment characteristics-based, flexible geometry characteristics-based, and flexible real-time modifications-based. Then, we provide a comprehensive overview of their fundamental characteristics, potential, and challenges. Furthermore, we demonstrate three vital enablers for the flexible MIMO technology, including efficient channel state information (CSI) acquisition schemes, low-complexity beamforming design, and explainable artificial intelligence (AI)-enabled optimization. Within these areas, eight critical sub-enabling technologies are discussed in detail. Finally, we present two case studies-pre-optimized irregular arrays and cell-free movable antennas-where significant potential for flexible MIMO technologies to enhance the system capacity is showcased.