This is usually a scale model aircraft (the exceptions are reconnaissance aircraft purpose made); controlled remotely using a hand held transmitter, which in turn sends a signal to a corresponding receiver which controls the servos on the aircraft to adjust the necessary rudders and wing flaps.
Radio controlled scale model aircraft come in various sizes, some are very basic with the purpose purely on flight and manoeuvrability. Whilst for obvious reasons all do need these anyway, some are built to be highly detailed replicas of the original plane. This may be for the love of the aircraft and attention to detail, or to be used in photo or film shoots, which can be used very effectively in historical films or documentaries. (Although there’s no denying CGI technology is probably now more widely used.)