The vertex algebras W(2,2) and W(2,4) are vertex algebras generated by two vectors of conformal weights 2 and 2 and by two vectors of weights 2 and 4, respectively. One from the first family is the vertex algebra associated to the Galilean conformal algebra first studied by Dong-Zhang and one from the second family is the Z_2 orbifold of the Heisenberg vertex operator algebra first studied by Dong-Griess. I will recall their representation theory and describe the subcategories of C_1-cofinite modules and show they admit braided tensor categories. Then I will discuss their fusion rules and prove the rigidity. I will also describe their connections to the quantum group tensor categories. This is based on the joint works with D. Adamovic, X. Lin, G. Radobolja and M. Peng.