The reader of the chapter will be able to connect techniques from machine learning (ML) and digital twins (DTs) to gain insights for monitoring and control of (dynamic) security for electrical power systems. DTs are validated and verified high-fidelity (hf) models providing high simulation accuracy. DTs can be used for simulation of the supervised process of system operation and are therefore able to provide synthetic studied data, where measurement data are scarce. However, for some real-time applications in monitoring and control, such high-fidelity simulation models are not appropriate due to the corresponding computational barrier. There, ML aims to create an application-specific, low-fidelity (lf) approximation of the digital twin. Such trained lf models are used in real-time applications where computational time is scarce and lf information is sufficient. The conceptual intersection of hf and lf models has been little explored and becomes increasingly complex. This chapter aims to provide a conceptual overview of how such hf and lf models can be combined. This chapter is split into two parts where the first part is to introduce ML, lf models, and digital twins, hf models, for power systems analysis, and the second chapter is to use these two types of models to form purpose-driven surrogate lf models, illustrated on the example of dynamic security assessment (DSA). In the first part, the concepts for using DTs as hf models for online power system studies and their corresponding tuning of model parameters are introduced. Subsequently, ML i.e., lf models, are introduced and their corresponding training frameworks.