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This review paper presents historical perspectives, recent advances and future directions in the multidisciplinary research field of plasma nanoscience. The current status and future challenges are presented using a three-dimensional framework. The first and the largest dimension covers the most important classes of nanoscale objects (nanostructures, nanofeatures and nanoassemblies/nanoarchitectures) and materials systems, namely carbon nanotubes, nanofibres, graphene, graphene nanoribbons, graphene nanoflakes, nanodiamond and related carbon-based nanostructures; metal, silicon and other inorganic nanoparticles and nanostructures; soft organic nanomaterials; nano-biomaterials; biological objects and nanoscale plasma etching. In the second dimension, we discuss the most common types of plasmas and plasma reactors used in nanoscale plasma synthesis and processing. These include low-temperature non-equilibrium plasmas at low and high pressures, thermal plasmas, high-pressure microplasmas, plasmas in liquids and plasma-liquid interactions, high-energy-density plasmas, and ionized physical vapour deposition as well as some other plasma-enhanced nanofabrication techniques. In the third dimension, we outline some of the 'Grand Science Challenges' and 'Grand Socio-economic Challenges' to which significant contributions from plasma nanoscience-related research can be expected in the near future. The urgent need for a stronger focus on practical, outcome-oriented research to tackle the grand challenges is emphasized and concisely formulated as from controlled complexity to practical simplicity in solving grand challenges. [ABSTRACT FROM AUTHOR]