## 1 Introduction  
High-altitude platforms (HAPs), such as satellites and unmanned aerial vehicles (UAVs), are critical components of non-terrestrial networks (NTNs). HAPs operate at altitudes exceeding 20 km, surpassing traditional terrestrial networks (TNs), and possess the unique ability to transcend geographical barriers. As essential elements of NTNs, HAPs drive the advancement of wireless communication beyond terrestrial constraints, promising comprehensive coverage, enhanced connectivity, and adaptable functionality [1; 2; 3; 4]. They are crucial in bridging the communication gap between remote or challenging terrains and enable diverse applications, ranging from aerial base stations (BSs) to cellular-connected NTNs [5; 6; 7; 8; 9]. In wireless communications, HAPs offer a strategic advantage due to their superior signal propagation capabilities and expanded coverage. This unique spatial positioning, combined with the flexibility of UAVs, makes HAPs dynamic and adaptive assets in the wireless communication arsenal [10]. Their deployment enriches NTN architectures, meeting the growing demand for connectivity in rural, oceanic, and challenging environments where terrestrial stations struggle to perform optimally [11]. This transformative impact of HAPs helps to address key challenges faced by terrestrial BSs. In scenarios with inadequate or compromised terrestrial infrastructure, HAPs offer agile and efficient solutions, ensuring uninterrupted connectivity. Their mobility and adaptability are particularly beneficial in emergencies, crowded events, or remote areas [12]. By serving as aerial base stations (BSs), HAPs redefine the concept of on-demand assistance to cellular networks, overcoming limitations associated with traditional TNs. The dynamic and unpredictable nature of non-terrestrial BSs underscores the need for advanced coverage optimization solutions, highlighting the critical role of HAPs in the NTN landscape [13]. Machine learning (ML) algorithms are used in contrast to traditional mathematical optimization methods. This approach has become essential for efficiently managing resources and mobility in HAP stations. HAPs, acting as intelligent agents, leverage ML techniques within Markov Decision Processes to optimize trajectories of aerial platforms, deliver specific services, and meet demanding performance standards. This shift towards ML-driven control strategies reflects the evolving complexity of NTN communications, encompassing a broader range of non-terrestrial platforms beyond UAVs. These advancements underscore the significance of integrating ML into NTN architectures to enhance efficiency and adaptability in non-terrestrial communication systems [14; 15; 16]. Reconfigurable intelligent surfaces (RISs) have recently emerged as a key enabling technology for 6G networks due to their capability to optimize wireless propagation environment, offering extended network coverage in a cost-effective manner. Integrating RISs into HAPs offers significant advantages, particularly in enhancing connectivity. Figure 1 depicts the scenario involving connectivity, where RISs control the phase of the incident signal, using one radio frequency (RF) chain to enhance the signal-to-noise ratio (SNR). As crucial relays between deep space networks (DSNs) and TNs, RISs facilitate efficient communication for interplanetary and Earth-orbiting missions, improving overall communication reliability and efficiency [17; 18]. RIS-assisted HAPs provide significant advantages in coverage, connectivity, and energy efficiency. The dense deployment of HAP systems extensively enhances ground coverage, effectively eliminating coverage gaps and ensuring continuous connectivity, especially during handoff processes involving low-Earth-orbit (LEO) satellites [19]. This paper provides a comprehensive survey of RIS-assisted NTN-based 6G communications. The main novelty of our work is highlighted through addressing the following key questions:  
1. What is RIS technology and how does it integrate with HAP systems? 2.