The year 2014 marks the first decade of the rise of graphene. Graphene, a single atomic layer of carbon atoms in sp2 bonding configuration having a honeycomb structure, has now become a well-known and well-established material. Among some of its many outstanding fundamental properties, one can mention a very high carrier mobility, a very large spin diffusion length, unsurpassed mechanical properties as graphene is the strongest material ever measured and an exceptional thermal conductivity scaling more than one order of magnitude above that of copper. After the first years of the graphene rush, graphene growth is now well controlled using various methods like epitaxial growth on silicon carbide substrate, chemical vapour deposition (CVD) or plasma techniques on metal, insulator or semiconductor substrates. More applied research is now taking over the initial studies on graphene production. Indeed, graphene is a promising material for many advanced applications such as, but not limited to, electronic, spintronics, sensors, photonics, micro/nano-electromechanical (MEMS/NEMS) systems, super-capacitors or touch-screen technologies. In this context, this Special Issue of the Journal of Physics D: Applied Physics on graphene reviews some of the recent achievements, progress and prospects in this field. It includes a collection of seventeen invited articles covering the current status and future prospects of some selected topics of strong current interest. This Special Issue is organized in four sections.The first section is dedicated to graphene devices, and opens with an article by de Heer et al on an investigation of integrating graphene devices with silicon complementary metal─oxide─semiconductor (CMOS) technology. Then, a study by Svintsov et al proposes a lateral all-graphene tunnel field-effect transistor (FET) with a high on/off current switching ratio. Next, Tsukagoshi et al present how a band-gap opening occurs in a graphene bilayer by using a perpendicular electric field to operate logic gates. Plaçais et al then show the realization of graphene microwave nano-transistors that are especially suitable for fast charge detectors. Matsumoto et al describe next some interesting graphene-based biosensor applications, while the following article by Otsuji et al shows recent advances in plasmonics in terahertz device applications. This section ends with the Dollfus et al article dealing with non-linear effects in graphene devices investigated by simulation methods.The second section concerns the electronic and transport properties and includes four articles. The first one by Gurzadyan et al provides an investigation of graphene oxide in water by femtosecond pump─probe spectroscopy to study its transient absorption properties. Jouault et al then review the quantum Hall effect of self-organized graphene monolayers epitaxially grown on the C-face of SiC. Next, Petkovic et al report on the observation of edge magneto-plasmons in graphene. Finally, Roche and Valenzuela focus on the limits of conventional views in graphene spin transport and offer novel perspectives for further progress.The third section addresses graphene tailoring and functionalization as studied by Genorio and Znidarsic for graphene nanoribbons, or by atomic intercalation as shown by the two articles from Starke and Forti, and from Bisson et al.The last section is devoted to graphene growth and morphology. Ogino et al first describe a method to grow graphene on insulating substrates using polymer films as a carbon source. Then, Suemitsu et al show the recent progresses in epitaxial graphene formation on cubic silicon carbide thin films. Finally, Norimatsu and Kusunoki investigate the structural properties and morphology of epitaxial graphene grown on hexagonal silicon carbide substrates by using a high-resolution transmission electron microscope, their article closing this Special Issue .