We study steady, radial gas outflows from galaxies in an effort to understand the way tenuous and hot gas is transported to large distances away from galaxies. In particular, we obtain solutions for outflow problems, and study the outflow topology, effects of the galaxy mass, the size of outflow regions, the efficiency of radiative cooling, and the fate of the cooled gas. Under general power-law forms for the cooling function and the gravitational field of galaxies, we show that the outflow solutions are determined by the two-parameter initial conditions. In an analogy with stellar wind or accretion problems, we demonstrate that there exists no transonic flow, but either subsonic or supersonic flows are obtainable. Solutions of the supersonic outflows are studied in detail as they are most likely to carry gas to large distances away from galaxies. We find that if gravity is weak, the outflow is characterized by the ratio of the radiative cooling time to the flow time, $t_c/t_f$. The importance of the galactic gravitational field is characterized by the fractional energy lost radiatively within the flow time in outflows with velocity equal to the circular velocity of the galaxy; if the fraction is small, gravity stops the outflow before the gas has a chance to cool radiatively. In the case the gas does cool radiatively, the cooled gas is most likely to form clouds via various instabilities. The clouds coast farther away from the galaxy because of the finite kinetic energy they inherit. We find that the hot gas in dwarf galaxies can either flow out as galactic winds, or cools radiatively to form clouds. In the latter case, the clouds escape the galaxies. In contrast, massive galaxies like our own tend to confine the gas. We present the surface brightness in various x-ray energy bands. We also estimate the mean