Micro Aerial Vehicles (MAVs) have seen a dramatic growth in the consumer market because of their ability to provide new vantage points for aerial photography and videography. However, there is little consideration for physical interaction with the environment surrounding them. Onboard manipulators are absent, and onboard perception, if existent, is used to avoid obstacles and maintain a minimum distance from them. There are many applications, however, which would benefit greatly from aerial manipulation or flight in close proximity to structures. This work is focused on facilitating these types of close interactions between quadrotors and surrounding objects. We first explore high-speed grasping, enabling a quadrotor to quickly grasp an object while moving at a high relative velocity. Next, we discuss planning and control strategies, empowering a quadrotor to perch on vertical surfaces using a downward-facing gripper. Then, we demonstrate that such interactions can be achieved using only onboard sensors by incorporating vision-based control and vision-based planning. In particular, we show how a quadrotor can use a single camera and an Inertial Measurement Unit (IMU) to perch on a cylinder. Finally, we generalize our approach to consider objects in motion, and we present relative pose estimation and planning, enabling tracking of a moving sphere using only an onboard camera and IMU.