Wireless communications systems are impacted by multi-path fading and Doppler shift in dynamic environments, where the channel becomes doubly-dispersive and its estimation becomes an arduous task. Only a few pilots are used for channel estimation in conventional approaches to preserve high data rate transmission. Consequently, such estimators experience a significant performance degradation in high mobility scenarios. Recently, deep learning has been employed for doubly-dispersive channel estimation due to its low-complexity, robustness, and good generalization ability. Against this backdrop, the current paper presents a comprehensive survey on channel estimation techniques based on deep learning by deeply investigating different methods. The study also provides extensive experimental simulations followed by a computational complexity analysis. After considering different parameters such as modulation order, mobility, frame length, and deep learning architecture, the performance of the studied estimators is evaluated in several mobility scenarios. In addition, the source codes are made available online in order to make the results reproducible.