Since the early stage of the development, quantum theory is bizarre: in trying to understand it, we had to forgive everything we know about causality, reality, certainty and so on. This is a completely different world, ruled by its own probability law. Neutron interferometry is one of the most suitable strategies to study quantum mechanics, where quantum interference effect of matter waves can be observed in a macroscopic scale. Starting with 4 -periodicity of spinor wave function, quantum phenomena such as gravitational effect on the wave function, superposition of spinor wave function, topological effect in quantum evolutions, were confirmed experimentally. Recently we accomplished neutron optical experiments concerning noncontextual hidden-variable theories, which are a kind of the hidden variable models of quantum mechanics, like local hidden variable theories, trying to give realistic view of quantum phenomena. Entangled states between degrees of freedom in single neutrons are exploited: violation of a Bell-like inequality, Kochen-Specker-like phenomena, quantum tomography, and further studies of triple-entanglements as well as Leggett's model were carried out. I am going to give an overview of these optical experiments with neutrons and discuss their future perspectives.