Usage of Unmanned Aerial Vehicles (UAVs) is growing rapidly in a wide range of consumer applications, as they prove to be both autonomous and flexible in a variety of environments and tasks. However, this versatility and ease of use also brings a rapid evolution of threats by malicious actors that can use UAVs for criminal activities, converting them to passive or active threats. The need to protect critical infrastructures and important events from such threats has brought advances in counter UAV (c-UAV) applications. Nowadays, c-UAV applications offer systems that comprise a multi-sensory arsenal often including electro-optical, thermal, acoustic, radar and radio frequency sensors, whose information can be fused to increase the confidence of threat's identification. Nevertheless, real-time surveillance is a cumbersome process, but it is absolutely essential to detect promptly the occurrence of adverse events or conditions. To that end, many challenging tasks arise such as object detection, classification, multi-object tracking and multi-sensor information fusion. In recent years, researchers have utilized deep learning based methodologies to tackle these tasks for generic objects and made noteworthy progress, yet applying deep learning for UAV detection and classification is considered a novel concept. Therefore, the need to present a complete overview of deep learning technologies applied to c-UAV related tasks on multi-sensor data has emerged. The aim of this paper is to describe deep learning advances on c-UAV related tasks when applied to data originating from many different sensors as well as multi-sensor information fusion. This survey may help in making recommendations and improvements of c-UAV applications for the future.