I (MJMcC) started in simulation with work on analogue (analog) computers. They provided a natural link between physical (prototype) systems and their dynamic simulations. The block diagrams that represented the analogue configuration had, naturally, the same topology as the diagrams showing cause-effect relationships in the prototype.
As a result, component parts of the electronic hardware (integrators, summers, potentiometers) of the model and their real world counterparts were easily linked in the minds of the users in a way that the underlying differential equations that they shared did not. It was a very natural way for engineers to do simulation of dynamic systems which is not now widely used. Though the tools like Simulink (MATLAB) provide a powerful, if expensive, replacement
In the middle '60's and early '70's digital computers became capable of matching computational speed in numerical solution of differential equations. A range of digital analog simulators appeared (DAS, MIDAS, CIDAS) which could be given block diagrams as net lists and imitate the analogue machines. It then became apparent that the interpretive block structured form was inefficient and statement structured simulation tools (CSMP, CSSL, ACSL) appeared that took advantage of compilation to create faster code. On the way the ability to point at a bit of the simulation and recognise it as a replica of some real world component, to stick a voltmeter in and read the value of the relevant variable, to flip switches and hot wire the model as it was running all vanished. We did get away from scaling problems, so it wasn't all bad news! Things like flight simulators with really heavy computational loads hung on a bit longer, but virtually all are now digital.

Plant and Process Simulators.
If you want to make a simulator for a plant, process or item of equipment and want both a good quantitative model and something pictorial that you can use for education, operator training, improving yield or optimising performance, then consult McCann Science.