Neurons' primary function is to encode and transmit information in the brain and body. The branching architecture of axons and dendrites must compute, respond, and make decisions while obeying the rules of the substrate in which they are enmeshed. Thus, it is important to delineate and understand the principles that govern these branching patterns. Here, we present evidence that asymmetric branching is a key factor in understanding the functional properties of neurons. First, we derive novel predictions for asymmetric scaling exponents that encapsulate branching architecture associated with crucial principles such as conduction time, power minimization, and material costs. We compare our predictions with extensive data extracted from images to associate specific principles with specific biophysical functions and cell types. Notably, we find that asymmetric branching models lead to predictions and empirical findings that correspond to different weightings of the importance of maximum, minimum, or total path lengths from the soma to the synapses. These different path lengths quantitatively and qualitatively affect energy, time, and materials. Moreover, we generally observe that higher degrees of asymmetric branching- potentially arising from extrinsic environmental cues and synaptic plasticity in response to activity- occur closer to the tips than the soma (cell body).