I will present our theoretical studies of a new family of two-dimensional (2D) materials: black phosphorus and its corresponding group IV-VI isoelectronic materials. For black phosphorus, these results include its intrinsic, fundamental properties such as quasiparticle band gaps, excitons, and anisotropic thermal conductance, and further engineered properties such as strain-tunable anisotropic electrical conductance and realizing Dirac cones and graphene electronics. Beyond black phosphorus, we find that the corresponding group IV-VI isoelectronic materials (monolayer GeS, GeSe, SnS, and SnSe) are essentially ferroelectric materials and may exhibit dramatically enhanced piezoelectric effects; their characteristic piezoelectric coefficients are about two orders of magnitude larger than those of monolayer transition metal dichalcogenides (TMDCs) and conventional bulk piezoelectric materials. Most of our theoretical predictions have been confirmed by subsequent experiments and may ignite further research on fundamental science and applications.