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Abstract: Modelling transient effects in superconducting circuits is particularly challenging due to simultaneous non-linear, interdependent phenomena often characterized by time scales and dimensions differing by orders of magnitude. Electromagnetic, thermal, and mechanical transients develop in superconducting filaments, strands, cables, magnet structures, and other elements composing the magnet electrical circuit, such as power sources, protection devices, and current leads. Several programs aimed at modelling electrical, electromagnetic, and thermal transients in superconducting magnets and circuits were developed as part of the STEAM (Simulation of Transient Effects in Accelerator Magnets) framework. The software suite includes software to simulate quench in superconducting magnets and circuits, either self-protected or protected by energy extraction, quench heaters, CLIQ, or a combination of these. Some of the programs use finite‑difference (FD) solvers for multipole and solenoid (LEDET, both 2D and 3D) and canted cos‑theta (ProteCCT) magnets. These programs include physics-driven methods for filament magnetization, coupling losses or eddy currents in metallic magnet components. Other programs use the finite‑elements (FE) solvers and include functionality to automatically generate simulation models of multipole, canted cos‑theta or high-temperature pancake coils (FiQuS in 2D or 3D) or multipole magnets (SIGMA in 2D). Other programs are dedicated to simulating quench in busbars with FD (LEDET, PyBBQ) or FE (BBQ) solvers. The STEAM models use a common, text-based (YAML) input file type to easily control, version, and maintain the model inputs. Increasingly, all the programs use the same material functions, coded in C and compatible with tool-specific programing language. Finally, different programs for modelling specific problems can be coupled with a cooperative simulation (COSIM). A library of models of most LHC and HL-LHC superconducting circuits was systematically developed, validated, and versioned. A few example transients modelled by STEAM tools are presented, covering many magnet types, conductor parameters, and quench protection systems. The STEAM framework is offered to the community as a flexible, effective, and computationally-efficient software package.