This paper addresses vision-based localization and servoing for quadrotors to enable autonomous perching by hanging from cylindrical structures using only a monocular camera. We focus on the problems of relative pose estimation, control, and trajectory planning for maneuvering a robot relative to cylinders with unknown orientations. We first develop a geometric model that describes the pose of the robot relative to a cylinder. Then, we derive the dynamics of the system, expressed in terms of the image features. Based on the dynamics, we present a controller which guarantees asymptotic convergence to the desired image space coordinates. Finally, we develop an effective method to plan dynamically-feasible trajectories in the image space, and we provide experimental results to demonstrate the proposed method under different operating conditions such as hovering, trajectory tracking, and perching.