In this talk, we prove that the canonical model of a 3-fold of general type with geometric genus 2 and with minimal canonical volume 1/3 must be a hypersurface of degree 16 in P(1,1,2,3,8), which gives an explicit description of its canonical ring. This implies that the coarse moduli space M_{1/3,2}, parametrizing all canonical 3-folds with canonical volume 1/3 and geometric genus 2, is an irreducible variety of dimension 189. Parallel studies show that M_{1,3} is irreducible as well and is of dimension 236, and that M_{2,4} is irreducible and is of dimension 270. As being conceived, every member in these three families is simply connected. Additionally, our method yields the expected Noether inequality for 3-folds of general type with p_g between 5 and 10, which completely solves all remaining cases of the Noether inequality for 3-folds. This is a joint work with Meng Chen and Chen Jiang.