Reconfigurable intelligent surfaces (RIS) have the immense ability to enhance the data transmission from the sender to the receiver. RIS is made of low-cost meta-surfaces that can reflect or refract the signals in the desired manner. The concept of RIS is inspired by a smart radio environment or programmable radio environment. Though the device was introduced a couple of years back, it has gained immense attention from researchers because of its applications in 5G and 6G wireless communications. The introduction of this device in wireless communications aids in reducing the hardware requirements, energy consumption, and signal processing complexity. The integration of this device with various emerging technologies such as multiple-input multiple-output (MIMO) systems, non-orthogonal multiple access (NOMA) technique, physical layer security, etc., has increased its potentiality in terms of performance enhancement. One such integration could be studied, i.e. RIS-assisted unmanned aerial vehicles (UAVs). The UAVs exhibit aiding capability in various services to our society such as real-time data collection, traffic monitoring, military operations & surveillance, medical assistance, and goods delivery. Despite the positive appeal, the UAV has its limitations such as fuel efficacy, environment disturbances, limited network capability, etc. Considering these scenarios, the RIS can provide assistance to UAVs to enhance their performance when integrated. There is a limited number of articles and researches that consider UAV-assisted RIS systems. This article provides a detailed survey on RIS-assisted UAV systems considering multiple contexts such as optimization, communication techniques, deep reinforcement learning, secrecy performance, efficiency enhancement, and the internet of things. Finally, we draw attention to the open challenges and possible future directions of UAV-assisted RIS systems in phase shifting, channel modeling, energy efficacy, and federated learning.