<p>Lighter-than-air vehicles (LTAVs), including airships, have gained renewed interest for applications in environmental monitoring, surveillance, and cargo transport due to their endurance, fuel efficiency, and ability to operate in remote environments. Despite these advantages, widespread adoption is hindered by challenges in accurate modeling and autonomous control under dynamic and uncertain conditions. This paper provides a comprehensive survey of LTAV control strategies, organizing them along two axes: (i) the degree of model dependence (model-free, model-aided, model-based) and (ii) the design paradigm (classical/linear, nonlinear-analytic, data-driven, learning-based). Classical methods are discussed in the context of their reliance on simplified and vehicle-specific models, with an emphasis on their limitations in adapting to nonlinear, time-varying dynamics and external disturbances. Data-driven/learning-based methods, including reinforcement learning and model-free adaptive control, are presented as promising alternatives for addressing these challenges. These approaches offer adaptability and robustness but face constraints related to computational demands, stability guarantees, and real-world validation. The survey explores state-of-the-art implementations of unmanned aerial vehicles and LTAVs, highlighting research gaps such as the need for robust, real-time adaptive controllers that bridge classical stability with machine learning flexibility. The paper concludes by outlining future research directions aimed at enabling fully autonomous LTAVs capable of reliable operation in complex and uncertain scenarios. This work synthesizes insights from classical and modern techniques, providing a foundational resource for advancing the field of autonomous airship modeling and control.</p>