In most books of fluid mechanics or specifically of turbulence, it is very common to find entire chapters dedicated to the analysis of turbulent shear flows interacting with solid walls whose surface is either smooth or rough. The case of permeable walls is instead almost never mentioned, yet it is very often encountered in many environmental and industrial contexts. Examples include rivers with granular beds, atmospheric boundary layers over snowpacks, densely packed urban areas and vegetated surfaces, catalytic reactors and heat exchangers of open-cell metal foam, to name just a few. The problems that are of interest when dealing with such flows relate to the modelling of flow resistance and scalar-transport processes occurring at the fluid-wall interface. Both problems are enormously affected by the mutual interaction between the fluid inside and outside the permeable wall, which is ultimately responsible for generating turbulent flows displaying counterintuitive and fascinating characteristics. This talk will provide an overview of these characteristics as discovered by the author while studying, mainly by means of experimental research, turbulent friction in flows over granular beds, drag and turbulent wakes generated by permeable obstacles and, as recently investigated, channel flows over permeable walls with suction.