In spite of the fact that single crystals of BaTiO3 of high quality can be grown since long time the properties of BaTiO3 and the mechanism of its main phase transition at TC are still intensively investigated. Complex physical mechanisms leading to the ferroelectric transition at TC have been investigated through the structural, thermal, optical, lattice dynamics, dielectric, elastic, domain structure and electromechanical properties. The representative results of these investigations will be summarised, and new data of the piezoelectric properties of single crystal BaTiO3 will be presented. The memristive behaviour - as promising effect for applications in micro-electronics and connected with the reversible transformation from a non-conducting to a metallic state - has opened another wide range of investigations. It was found that such a transformation cannot be described in terms of point defect chemistry only. We will explain that highly conducting extended defects play dominant role in the case of the memristive behaviour, and can help to understand such phenomena as self-polarization effects, aging phenomena, fractal shape of ferroelectric domains, screening effects, leakage currents and/or electrically induced chemical transformations in the surface region. We believe that understanding the physical and chemical properties of the extended defects at the nanoscale may allow to accept an hypothesis that true barium titanate crystals are a kind of a natural composite. That is why the statement that “… a clean, free ferroelectric surface in BaTiO3 /…/ may be regarded as a ferroelectric metal“ is in our opinion an oxymoron.