This work presents a review of studies of the Martian magnetic fields during the early Soviet missions to Mars in 1971–1974, which never approached Mars by closer than 1000 km before the experiment with the Magnetometer/Electronic Reflectometer (MAG/ER) on board the Mars Global Surveyor spacecraft, which could descend to altitudes of 80–100 km. At present, the experiment with the magnetometer (MAG) onboard the American MAVEN spacecraft adds new data, but the map of distribution of remnant magnetic fields of Mars and the picture of their interaction with the solar wind are already formed and, at its core, obviously, will not be revised. Thus, it would be very instructive to consider the following in detail: (a) what is already known regarding the features and distribution of remnant magnetic fields on Mars; (b) how they control the interaction of solar wind with a weakly magnetized planet (Mars); and (c) what is its distinction from another nonmagnetized planet (Venus).