Surface ramps in normal fault zones of the Iceland plate boundary have been described in many studies, but their structure and evolution are not well understood. We show that surface ramps are manifestations of large tilted blocks (TBs) formed in dip relays of normal faults. Based on existing modeling studies, we propose three classes of TBs defined by kinematics and location of the hinge of the TB. TBs are considered a member of the family of fault relay structures that form near the surface, commonly, but not exclusively, in columnar basalts with orthotropic strength. We present high-resolution aerial vehicle–based observations of a representative set of normal faults in Iceland and compare these with geometric models we derived from modeling studies. We predict extensive tectonic cave (fluid conduit) systems under the TB, which interact with magma and groundwater flow. The general fault structure is dominated by large, subvertical open fractures reactivating cooling joints that are locally filled by basalt rubble. We propose the existence of a hybrid failure zone at larger depths before the effective vertical stress is sufficient to initiate shear fractures in intact basalt.