We present SDO/AIA observations of an eruptive X-class flare of 2012 July 12, and compare its evolution with the predictions of a three-dimensional (3D) numerical simulation. We focus on the dynamics of flare loops that are seen to undergo slipping reconnection during the flare. In the Atmospheric Imaging Assembly (AIA) 131 Å observations, lower parts of 10 MK flare loops exhibit an apparent motion with velocities of several tens of km s-1 along the developing flare ribbons. In the early stages of the flare, flare ribbons consist of compact, localized bright transition-region emission from the footpoints of the flare loops. A differential emission measure analysis shows that the flare loops have temperatures up to the formation of Fe XXIV. A series of very long, S-shaped loops erupt, leading to a coronal mass ejection observed by STEREO. The observed dynamics are compared with the evolution of magnetic structures in the "standard solar flare model in 3D." This model matches the observations well, reproducing the apparently slipping flare loops, S-shaped erupting loops, and the evolution of flare ribbons. All of these processes are explained via 3D reconnection mechanisms resulting from the expansion of a torus-unstable flux rope. The AIA observations and the numerical model are complemented by radio observations showing a noise storm in the metric range. Dm-drifting pulsation structures occurring during the eruption indicate plasmoid ejection and enhancement of the reconnection rate. The bursty nature of radio emission shows that the slipping reconnection is still intermittent, although it is observed to persist for more than an hour.