Two-dimensional (2D) crystalline (semi)conductors, inspired by model systems such as graphene, silicenes and transition metal dichalcogenides, are a central topic of current research at the nanoscale. Exciting physical properties such as massless fermions, fractional quantum hall effects and flat-band ferromagnetism originate from the unique electronic band structures of these materials. Conductive 2D metal-organic frameworks (MOFs) are a recent and promising addition to these classes of materials due to features such as bottom-up tailorability and guest-accessible nanoporosity. Here, were present a new highly tunable platform of square-symmetry conductive MOFs. The electronic band structure of these materials is unique relative to the more common hexagonal (honeycomb) symmetry that characterizes many 2D materials and all previously reported π-conjugated MOFs. We will discuss the experimental and first-principles calculated physical properties of these new materials in relation to the hexagonal phases.