This survey paper discusses the fundamentals of power systems modelling in the presence of large amounts of converter-interfaced generation (CIG). By referring to real-life events characterised by anomalous dynamics associated to the presence of CIG, the concepts of narrow versus broad band signals are first recalled along with the limitation of the meaning of apparent power, power factor and reactive power. In this regard, the adequacy of the phasor representation of voltages and currents waveforms is thoroughly discussed. Then, with respect to the central subject of control of power converters, a revised definition of grid-following and grid-forming converters is provided along with a thorough discussion of their associated controls and a comprehensive classification for both classes of converters. Several applications inspired by actual case studies are included in the paper in order to provide realistic application examples.