Natural phenomena, such as thermal soaring of birds, gravitational settling of inertial particles in turbulent flows and acrobatic feats performed by flying insects, can inspire interesting and sometimes useful solutions to the sensing and control problems of micro aerial vehicles (MAVs). This dissertation covers novel biologically inspired MAV sensing and control approaches that are efficient and robust in the presence of unforeseen wind disturbances and modeling uncertainties. At first, this dissertation presents a new feedback control approach inspired by experimental studies on particle transport that have recently illuminated particles' ability to traverse homogeneous turbulence through the so-called fast-tracking effect. While in nature fast-tracking is observed only in particles with inertial characteristics that match the flow parameters, the new fast-tracking feedback control approach employs available propulsion and actuation to allow the vehicle to respond to the surrounding flow in the same manner as ideal fast-tracking particles would. The resulting fast-tracking closed-loop controlled vehicle is then able to leverage turbulent flow structures, such as sweeping eddies, to reduce travel time and energy consumption. The fast-tracking approach is shown to significantly outperform existing optimal control solutions, such as linear quadratic regulator and bang-bang control, and to be robust to changes in the vehicle characteristics and/or turbulent flow parameters. Furthermore, since this fast-tracking control design requires prior knowledge of the turbulent flow parameters, this dissertation presents a novel approach of using noisy on-board measurements to estimate the flow parameters via the sparse identification of nonlinear dynamics (SINDy) method. In addition to particle transport theory, MAV sensing and control strategies can be extracted from biological neural systems. Since spiking neural networks (SNNs) encode information in sequences of spike times, spike train decoding is considered one of the grand challenges in reverse-engineering neural control systems as well as in the development of neuromorphic controllers. Therefore, this dissertation presents a novel relative-time-kernel-based spike train decoding approach that accounts for not only individual spike train patterns, but also the relative spike timing between neuron pairs in the population. Using the data collected in hawk moth's flower tracking experiments, the new spike train decoding method allows us to uncover the precise mapping from the spike trains of ten primary flight muscles to the resulting forces and torques on the moth body. The new relative-time-kernel-based spike train decoder significantly improves the prediction of the resulting forces and torques when compared to the existing instantaneous-kernel-based and rate-based decoders. Finally, inspired by the insect's flapping flight control strategies, this dissertation presents a novel two-phase adaptive full-envelope SNN control design for flapping-wing micro aerial vehicles (FWMAVs) that is able to learn and adapt to unmodeled uncertainties online. During the offline learning phase, populations of spiking neurons are trained by supervised learning to approximate a gain-scheduled proportional-integral-filter (PIF) compensator developed to stabilize the ideal vehicle dynamic model. The online learning phase improves the performance subject to actual vehicle dynamics by incrementally updating the neural connection weights via policy gradient reinforcement learning (PGRL). This two-phase adaptive SNN control design is then implemented for the control of a simulated insect-scale flapping-wing robot known as RoboBee over its full flight envelope. The adaptive SNN controller is shown to outperform a benchmark non-adaptive SNN controller when the RoboBee is commanded to conduct a full range of maneuvers in the presence of significant uncertainties, such as parameter variations, unmodeled dynamics and measurement errors, as well as actuator failures. The bio-inspired sensing and control approaches presented in this dissertation can be potentially implemented on the next generation of smart, agile and highly adaptive MAVs.