The term "mud volcano system" is coined to describe the set of structures associated with a constructional edifice (mud volcano) and feeder complex that connects the volcano to its source stratigraphic unit. Three-dimensional (3-D) seismic data from the South Caspian Basin are used to investigate the structural elements and evolution of these systems. Mud volcano systems initiate via early, kilometer-biconic edifices termed "pioneer" cones. These are fed by fluscale, idization pipes tens of meters in width. Subsequent kilometer-scale mud volcanoes grew via persistent extrusion, fed by numerous additional fluidization pipes injected in the country rock. This subvolcanic intrusion complex creates a densely intruded, cylindrical similar in cross section to gryphon swarms observed at an outzone, crop onshore. Wall rock erosion and compaction of the intruded zone leads to the collapse of a downward-tapering cone enveloping the cylindrical zone, capped by ring faults that define a kilometer-scale caldera that downthrows the overlying mud volcano. Mud volcanoes get buried during basin subsidence and can look like intrusive laccoliths at first glance on seismic data. Reactivation of mud flow through a conduit system generates a stack of superimposed mud volcanoes through time. Large volcanoes continue to dewater during burial and may locally remobilize. This model of mud volcano evolution has similarities with igneous and salt tectonic systems. To reduce drilling and geologic uncertainty, mud volcano system extent and impacts on a reservoir can be assessed on 3-D seismic data.