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Since its discovery in the late 90s we have witnessed important advances in the study and characterisation of the Anomalous Microwave Emission, from both theoretical and observational perspectives. Recently WMAP and Planck data have provided a wealth of information in a sufficiently high number of Galactic regions as to allow, for the first time, studying the physical properties associated with this phenomenon in a statistical way. Although electric dipole emission from spinning dust grains seems to provide the best explanation to the observed data, alternative models are also able to provide reasonably good fits to the data. There are also other open questions like what are exactly the AME carriers. Although PAHs have long been thought to be the AME carriers, the recently-found anticorrelation between AME intensity and PAH abundances has casted doubts on this hypothesis. This has recently led to considering alternative nanoparticles like the hydrocarbons carriers of diffuse interstellar bands, silicate or iron nanograins, or even nanodiamonds. Furthermore, it is currently unknown what is the level of AME polarisation, an aspect that is important in the light of ongoing experiments searching for the B-mode signal in the CMB polarisation. Following the same spirit as previous AME workshops (Manchester 2012, Caltech 2013, ESTEC 2016), in this fourth AME workshop that will be held in Tenerife on Friday, 19 October (same week as the conference “CMB foregrounds for B-mode studies”), we plan to bring together both AME theorists and observers to discuss the state of the art of the field, and to define what are the open questions and the future steps that are required to complete the picture that will allow us a better understanding of this phenomenon. The format of the workshop will consist in short talks followed by long open discussions.