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The pn junction is a fundamental electrical component in modern electronics and optoelectronics. Currently, there is a great deal of interest in the two-dimensional (2D) pn junction. Although many experiments have demonstrated the working principle, there is a lack of fundamental understanding of its basic properties and expected performances, in particular when the device is driven out of equilibrium. To fill the current gap in understanding, we investigate the electrostatics and electronic transport of 2D lateral pn junctions. To do so we implement a physics-based simulator that selfconsistently solves the 2D Poisson's equation coupled to the drift-diffusion and continuity equations. Notably, the simulator takes into account the strong influence of the out of plane electric field through the surrounding dielectric, capturing the weak screening of charge carriers. Supported by simulations, we propose a Shockley-like equation for the ideal current voltage characteristics, in full analogy to the bulk junction after defining an effective depletion layer (EDL). We also discuss the impact of recombination generation processes inside the EDL, which actually produce a significant deviation with respect to the ideal behavior, consistently with experimental data. Moreover, we analyze the capacitances and conductance of the 2D lateral pn junction. Based on its equivalent circuit we investigate its cut-off frequency targeting RF applications. To gain deeper insight into the role played by material dimensionality, we benchmark the performances of single-layer MoS2 (2D) lateral pn junctions against those of the Si (3D) junction. Finally, a practical discussion on the short length 2D junction case together with the expected impact of interface states has been provided. Given the available list of 2D materials, this work opens the door to a wider exploration of material dependent performances.