Furthering the field of synthetic organic chemistry from the discrete molecules regime to the extended structure regime, covalent organic frameworks (COFs) represent a new genre of crystalline porous materials featuring designability with molecular-level precision, well-defined porosity, and exceptional stability imparted by the robust covalent linkages reticulating organic molecules. The topology of COFs is a principal feature that regulates their functionality and usability for emerging technologies. Profound comprehension of network topologies and maneuvering them toward targeted applications are crucial to advancing the realm of COF research and developing novel functional materials for exciting breakthroughs. In this Perspective, we discuss the recent research pursuits contributing to the discovery of highly connected COF nets having novel topologies, assess the key challenges to achieving such network topologies, and offer insights into the current scenario and future directions.