Orbital maneuvers, in general, is an essential topic in astrodynamics and aerospace engineering for space mission planning and design. In particular, the use of natural forces to control the motion of a spacecraft is an interesting topic for research because it reduces the total cost of the mission. In that sense, the present paper surveys numerical solutions and mapping of space trajectories that use the atmosphere of Mars as a natural propulsion system to change the orbit of a spacecraft without using fuel or propellant. Several maneuvers are considered, such as aerocapture, aerobraking, orbital insertion, and close approach maneuvers to redirect the spacecraft to another orbit, etc. In all those cases, the main idea is to find trajectories that make the spacecraft to pass inside the atmosphere of Mars to use both drag and lift to control the resulting trajectory of the spacecraft. Drag always removes energy from the spacecraft; on the other hand, the lift can change the curvature angle above the planet. Those maneuvers can also be combined with other maneuvers based on propulsion to increase flexibility and to enlarge the number of possible applications.