The progress in the understanding of the physics and the concurrent parameter extension in the large helical device since the last IAEA-FEC, in 2012 (Kaneko O et al 2013 Nucl. Fusion53 095024), is reviewed. Plasma with high ion and electron temperatures (Ti(0) ∼ Te(0) ∼ 6 keV) with simultaneous ion and electron internal transport barriers is obtained by controlling recycling and heating deposition. A sign flip of the nondiffusive term of impurity/momentum transport (residual stress and convection flow) is observed, which is associated with the formation of a transport barrier. The impact of the topology of three-dimensional magnetic fields (stochastic magnetic fields and magnetic islands) on heat momentum, particle/impurity transport and magnetohydrodynamic stability is also discussed. In the steady state operation, a 48 min discharge with a line-averaged electron density of 1 × 1019 m−3 and with high electron and ion temperatures (Ti(0) ∼ Te(0) ∼ 2 keV), resulting in 3.36 GJ of input energy, is achieved.