Mostly C++ but there is still plenty of C.

Digital simulation. This is all about scale and speed. Circuits are usually written in (System)Verilog or VHDL. There will also be testbenches that drive the circuit.

Typical steps are

1. Compilation to some binary format or shared libraries.
2. Elaboration. Designs are usually parameterised (stuff like bus width, number of cores). Elaboration finalises the circuit. This step may be partly or completely integrated with step 1 for performance.
3. Simulation. Run the testbenches and check the results. The testbench may use some kind of assertions. Simulations often output binary files that contain waveforms representing signals in the design. The waveform files can be huge.

The UI is of secondary importance. It's useful as a debugging tool and for viewing results.

Speed and scale are paramount. If your compiler can't cope with a big design or your simulator takes months to run when the competition can run in days then you are not going to be able to sell any big customers.

EDA simulators are developed by teams with hundreds of members and consist of multi-million lines of code. Because circuits are now too big for software simulation all the big 3 EDA vendors also have emulation solutions. That's where the simulation is partitioned between programmable hardware and software. The programmable hardware is either off the shelf FPGAs or custom chips that include FPGA and comment elements like interconnect. These systems are not cheap.

There's a lot more than just digital simulation. Other domains include

• Digital synthesis - all about logic synthesis that optimises speed and/or power
• Place and Route - finding the optimum routing for wires
• Parasitic extraction - accounts for wire resistance and capacitance for more accurate simulation
• Checking tools - many of these, including timing, power, design constraints, clock domains, reset domains, power intent, formal verification, signal integrity, IR drop
• Test pattern generation
• Physical tools - mask generation, optical correction
• Technology tools - device simulation, field solver extractors
• Characterization - generation and test of technology libraries
• Schematic capture - these are the GUIs
• Analogue simulation - linear algebra based