The Cherenkov Telescope Array (CTA) is a worldwide new generation project aimed at realizing an array of a hundred ground based gamma-ray telescopes. ASTRI (Astrofisica con Specchi a Tecnologia Replicante Italiana) is the Italian project whose primary target is the development of an end-to-end prototype, named ASTRI SST-2M, of the CTA small size class of telescopes devoted to investigation of the highest energy region, from 1 to 100 TeV. Next target is the implementation of an ASTRI/CTA mini-array based on seven identical telescopes. Silicon Photo-Multipliers (SiPMs) are the semiconductor photosensor devices designated to constitute the camera detection system at the focal plane of the ASTRI telescopes. SiPM photosensors are suitable for the detection of the Cherenkov flashes, since they are very fast and sensitive to the light in the 300-700nm wavelength spectrum. Their drawbacks compared to the traditional photomultiplier tubes are high dark count rates, after-pulsing and optical cross-talk contributions, and intrinsic gains strongly dependent on temperature. Nonetheless, for a single pixel, the dark count rate is well below the Night Sky Background, the effects of cross-talk and afterpulses are typically lower than 20%, and the gain can be kept stable against temperature variations by means of adequate bias voltage compensation strategies. This work presents and discusses some experimental results from a large set of measurements performed on the SiPM sensors to be used for the ASTRI SST-2M prototype camera and on recently developed detectors demonstrating outstanding performance for the future evolution of the project in the ASTRI/CTA mini-array.