Switch mode power supplied that you find with phones etc. do still use transformers.
An old fashion large wall wart that runs the transformer at 50Hz (or 60Hz) to drop the voltage, these are large and bulky, plus have no brains so the output voltage is dependent directly on the input voltage and the number of turns. 60Hz through a 50Hz transformer at high load can also cause heating problems due to reactive power.
Switch mode supplies rectify mains AC to DC, then turn that into a high frequency AC (10kHz-50kHz or so) which is then dropped down using a small transformer. The higher the frequency, the smaller the transformer can be made (though the power capacity is also limited). These also support multiple voltages by using a feedback network (usually optically isolated) which adjusts either the frequency or duty cycle of the high frequency AC to result in constant output voltage regardless (within reason) of the input. In fact this is why sometimes you can hear them humming at high frequency when not connected to anything.
With motors, it depends on the type of motor. If it is a DC motor that runs at less than the lower 110V mains, you can use a similar technique with SMPS to regulate the rectified mains down to the correct voltage (frequency and voltage then don't matter).
If it is an AC motor, then you may have issues - especially if it needs to run at a specific RPM which will be governed by the mains frequency, and voltage. Now there are solutions to this. One that springs to mind is to use an inverter - basically the mains is rectified to DC to remove the frequency issue, and then an inverter is used to convert that back to a sine (ish?) wave of the correct frequency. With motors the inverter can also regulate the voltage using PWM because the inductance of the motor will filter away the PWM signal leaving a fairly constant amplitude sine wave (though again that only works if the motor is rated for <=110V).