Amorphous metal-organic frameworks (MOFs) are an emerging class of materials. However, their structural characterisation represents a significant challenge. Fe-BTC, and the commercial equivalent Basolite® F300, are MOFs with incredibly diverse catalytic ability, yet their disordered structures remain poorly understood. Here, we use advanced electron microscopy to identify a nanocomposite structure of Fe-BTC where nanocrystalline domains are embedded within an amorphous matrix, whilst synchrotron total scattering measurements reveal the extent of local atomic order within Fe-BTC. We use a polymerisation-based algorithm to generate an atomistic structure for Fe-BTC, the first example of this methodology applied to the amorphous MOF field outside the well-studied zeolitic imidazolate framework family. This demonstrates the applicability of this computational approach towards the modelling of other amorphous MOF systems with potential generality towards all MOF chemistries and connectivities. We find that the structures of Fe-BTC and Basolite® F300 can be represented by models containing a mixture of short- and medium-range order with a greater proportion of medium-range order in Basolite® F300 than in Fe-BTC. We conclude by discussing how our approach may allow for high-throughput computational discovery of functional, amorphous MOFs.