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We review recent compact modeling solutions for Organic and Amorphous Oxide TFTs (OTFTs and AOS TFTs, respectively), which were developed, under the framework of the EU-funded project DOMINO, to address issues specifically connected to the physics of these devices. In particular, using different approaches, analytical equations were formulated to model the Density of States (DOS), different transport mechanisms, trapping/de-trapping, drain current, stress, capacitances, frequency dispersion and noise. The final TFT models were, after implementation in Verilog-A, validated by means of the design and simulation of test circuits.