Investigating and Classifying Calabi-Yau manifolds is a subject of significant interest in algebraic geometry.  Thanks to Buchsbaum and Eisenbud, we know that a codimension 3 Gorenstein variety is given by pfaffians. In this talk I will speak about constructing, investigating and classifying non complete intersection codimension 3 Calabi-Yau threefolds in $P^2\times P^4$, $P^3\times P^3$, $P^1\times P^5$, $P^2\times P^2\times P^2$, $P^1\times P^1\times P^4$, $P^1\times P^2\times P^3$, $P^2\times P^2\times P^1\times P^1$, $P^3\times P^1\times P^1\times P^1$, $P^2\times P^1\times P^1\times P^1\times P^1$, $P^1\times P^1\times P^1\times P^1\times P^1\times P^1$.