The harmful effects of space radiation on astronauts is one of the most important limiting factors for human exploration of space beyond low Earth orbit, including a journey to Mars. This talk will present an overview of space radiation issues that arise throughout the solar system and will describe research efforts at NASA aimed at studying space radiation effects on astronauts, including the experimental program at the NASA Space Radiation Laboratory at Brookhaven National Laboratory. Recent work on galactic cosmic ray simulation at ground based accelerators will also be presented. The three major sources of space radiation, namely geomagnetically trapped particles, solar particle events and galactic cosmic rays will be discussed as well as recent discoveries of the harmful effects of space radiation on the human body. Some suggestions will also be given for developing a space radiation program in the Republic of Korea.