Insight-HXMT is the first Chinese X-ray astronomical mission, launched successfully on June 15, 2017, from China's Jiuquan Satellite Launch Center. Insight-HXMT was designed to have a broad energy coverage in Xrays, from 1-250 keV, with excellent timing and adequate energy resolution at soft X-rays, and the largest effective area at hard X-rays. This allows, in particular, to observe bright sources like X-ray binaries (XRBs) in their bright/outburst states with high cadence and high statistics at hard and soft X-rays at once. It was then expected that the Insight-HXMT mission will bring us new insights regarding the characteristics of several source classes. Examples include characterizing High-Mass X-ray Binaries (HMXBs) and the outburst evolution of Low-Mass X-ray Binaries (LMXBs). For instance, in HMXB systems, the region around their Alfven radius that is responsible to determine whether accretion or propeller occurs, or the region around the NS magnetic pole where the intense X-rays are supposed to be produced are specially appealing targets of study. For the LMXBs, the evolution the outburst and the properties of the compact objects themselves are obvious priority targets for Insight-HXMT. Due to the broad coverage in energy, Insight-HXMT is specially well suited to study the influence of thermonuclear (type-I) X-ray bursts upon the surrounding environment.Observations from Insight-HXMT are producing stateof-the-art samples in a broad energy band, covering both the timing and energetic domains. Besides, so far the largest effective area at MeV, i.e, in soft gamma-rays, of the anti-coincidence detector CsI of Insight-HXMT, provides an almost unique power in monitoring flare events like Gamma-Ray Bursts (GRBs), especially short/hard GRBs suggested to be generated in binary neutron star mergers. We are proud to present a collection of papers of the Journal of High Energy Astrophysics on the Early Results of China's 1st X-ray Astronomy Satellite Insight-HXMT.These papers cover the in-orbit performance, the background model, and all calibration results, which will serve as primary references of future observations and data analysis with Insight-HXMT, expected to operate in space for several more years to come. Then, the special issue contains details of instrument calibration, both in