ASTRI (``Astrofisica con Specchi a Tecnologia Replicante Italiana'') is a flagship project of the Italian Ministry of Education, University and Research. Within this framework, INAF is currently developing a wide field of view (9.6 degrees in diameter) end-to-end prototype of the CTA small-size telescope (SST), devoted to the investigation of the energy range from a few TeV up to hundreds of TeV, and scheduled to start data acquisition in 2014. For the first time, a dual-mirror Schwarzschild-Couder optical design will be adopted on a Cherenkov telescope, in order to obtain a compact (F# = 0.5) optical configuration.
A second challenging, but innovative technical solution consists of a modular focal plane camera based on Silicon photo-multipliers with a logical pixel size of 6.2mm$times$6.2mm. We will describe the current status of the project, the expected performance, and its possible evolution in terms of a SST mini-array. This CTA-SST precursor, composed of a few SSTs and developed in collaboration with CTA international partners, could peruse not only the technological solutions adopted by ASTRI, but also address a few scientific test cases that will be discussed in detail.