Who ya gonna call? No not Ghostbusters, although something very similar… a plumber.
Most problems with the toilet not flushing are as simple as the ball valve stuck against the cistern wall, or the water leaking from its seals and pouring into the cistern which is going out through the overflow. As the cistern wouldn’t flush the toilet bowl, it may become full through use and stop flushing, so even if the flush problem is fixed, it may not mean the bowl is clear. In this case, a simple rod and flat disc type plunger will sort this problem out.
But if the blockage is in the waste pipework leading from the bowl to the outside world, then the bowl will need to be removed from its pipework and sometimes removed from the cistern.
Most toilets are upstairs and have an external waste pipe called the stack pipe which is also used by a shower/bath/basin. If this pipe is blocked, then it is possible to sometimes unblock it from inside the house or outside from a manhole (access chambers) using jetting equipment.
Sometimes the blockage is some distance away in a neighbour’s garden. The neighbour may not even be aware of the problem at this stage, but jetting at least as far as the next manhole might solve the problem.
Terraced houses tend to have WC waste pipework that serves 3 houses running across gardens. The plumber will need to access this underground pipework, and if it’s daytime and the neighbours are at work, that’s when the plumber finds out which neighbours own pit bull terriers!