The development of new carbon materials with novel properties and excellent applications is essential and urgent in many fields, such as potassium-ion batteries (PIBs). In this study, a family of 30 two-dimensional biphenylene carbon allotropes (2D-BCAs) have been systematically extended in theory. The energies of these allotropes are slightly higher than that of graphene, which can be well described by a quantitative energy equation. The 2D-BCAs show high synthesizability consistent with the experimental biphenylene network via "HF-zipping" reactions. The 2D-BCAs are metallic or semimetallic. Six representative 2D-BCAs exhibit good lattice dynamical and thermal stability, excellent anisotropic mechanical properties, and ORR catalytic activity. Moreover, the selected 2D-BCAs demonstrate ultrahigh theoretical potassium-storage capacities of 1116-1489 mAh·g-1, low migration barriers of 0.03-0.22 eV, and low open-circuit voltages of 1.10-0.02 V. The remarkable properties render 2D-BCAs as promising anode materials in PIBs, electrocatalysts, and conductors in electronics and iontronics.