This chapter introduces a design guide of memristor emulator circuits, from conceptual idea until experimental tests. Three topologies of memristor emulator circuits in their incremental and decremental versions are analysed and designed at low and high frequency. The behavioural model of each topology is derived and programmed at SIMULINK under the MATLAB environment. An offset compensation technique is also described in order to achieve the frequency-dependent pinched hysteresis loop that is on the origin and when the memristor emulator circuit is operating at high frequency. Furthermore, from these topologies, a technique to transform normal non-linear resistors to inverse non-linear resistors is also addressed. HSPICE numerical simulations for each topology are also shown. Finally, three real analogue applications based on memristors are analysed and explained at the behavioural level of abstraction.