This paper studies the problem of air-to-air target following of micro aerial vehicles (MAVs) motivated by the application of defense against malicious MAVs. When the bearing of the target MAV has been measured by the onboard visual sensor of the pursuer MAV, the problem becomes three-dimensional (3-D) bearing-only target following, which has been rarely studied in the literature and faces some unique challenges. To solve this problem, we propose the following novel results. First, to estimate the motion of the target MAV from 3-D bearing measurements, we propose a new pseudo-linear Kalman filter, which has a concise expression and superior stability compared to the classic ones such as the extended Kalman filter and modified polar coordinate filter. Second, we propose a novel approach to analyze the observability of state estimation when only bearing information is available. While the existing approaches are applicable to 2-D and single-step time-horizon cases, ours can handle more general 3-D and multiple-step time-horizon cases. Third, based on the theoretical conclusion of our observability analysis, we design a new 3-D helical guidance law that can better exploit the additional degree of freedom in 3D. The guidance law is adapted to the quadcopter's dynamics and a low-level flight controller is designed based on geometric control. Numerical simulation results verify the superior performance of the proposed algorithms compared to the state-of-the-art ones. Flight experiments on real quadrotor platforms further show the effectiveness and robustness of the proposed algorithms in practice.