Self/Anti-Self Charge Conjugate States for j=1/2 and j=1

We briefly review recent achievements in the theory of neutral particles (the Majorana-McLennan-Case-Ahluwalia construct for self/anti-self charge conjugate states for j=1/2 and j=1 cases). Among new results we present a theoretical construct in which a fermion and an antifermion have the same intrinsic parity; discuss phase transformations and find relations between the Majorana-like field operator $\nu$, given by Ahluwalia, and the Dirac field operator. Also we give explicit forms of the $j=1$ ``spinors" in the Majorana representation.