Applications in high-voltage engineering are modelled and simulated by transient electroquasistatic and electrothermal finite-element methods. The model account for field- and temperature-dependent materials, field grading, thermal convection and heating, AC and DC excitation and polarity reversal. Recent results include the simulation of high-voltage AC metal-oxide arresters and high-voltage droplet generation. Current research aims at accomplishing the tools with uncertainty quantification and optimisation and at analysing high-voltage DC equipment.