This survey explores the application of learning-based methods in adaptive informative path planning (AIPP) for robotics. AIPP enables mobile robots to efficiently collect useful data about initially unknown environments. The paper provides a unified mathematical formulation for AIPP, establishes two complementary taxonomies of current work from the perspectives of learning algorithms and robotic applications, and discusses key challenges and future directions. It highlights the benefits of learning-based methods in AIPP frameworks, including adaptability, robustness, and scalability. The survey also reviews various learning techniques, such as supervised learning, reinforcement learning, imitation learning, and active learning, and their applications in AIPP. It discusses the challenges of AIPP, including modeling and predicting new information, balancing exploration and exploitation, and handling sensor and actuation uncertainties. The paper also addresses evaluation metrics, benchmark scenarios, and simulation environments used in AIPP research. It highlights the importance of learning-based methods in enabling more generally applicable and robust robotic data-gathering systems. The survey provides a comprehensive catalog of papers reviewed, including publicly available repositories, to facilitate future studies in the field. The paper concludes that learning-based methods offer a promising approach to address the challenges of AIPP, enabling more flexible, adaptive, and scalable solutions.This survey explores the application of learning-based methods in adaptive informative path planning (AIPP) for robotics. AIPP enables mobile robots to efficiently collect useful data about initially unknown environments. The paper provides a unified mathematical formulation for AIPP, establishes two complementary taxonomies of current work from the perspectives of learning algorithms and robotic applications, and discusses key challenges and future directions. It highlights the benefits of learning-based methods in AIPP frameworks, including adaptability, robustness, and scalability. The survey also reviews various learning techniques, such as supervised learning, reinforcement learning, imitation learning, and active learning, and their applications in AIPP. It discusses the challenges of AIPP, including modeling and predicting new information, balancing exploration and exploitation, and handling sensor and actuation uncertainties. The paper also addresses evaluation metrics, benchmark scenarios, and simulation environments used in AIPP research. It highlights the importance of learning-based methods in enabling more generally applicable and robust robotic data-gathering systems. The survey provides a comprehensive catalog of papers reviewed, including publicly available repositories, to facilitate future studies in the field. The paper concludes that learning-based methods offer a promising approach to address the challenges of AIPP, enabling more flexible, adaptive, and scalable solutions.