This paper presents molybdenum manufactured by Laser Powder Bed Fusion (LPBF) and the detrimental and positive effects of oxygen and carbon as its impurity and alloying element, respectively. The effects of manufacturing temperature, solidification mechanism, and grain boundary strength, are discussed. It was found that oxygen is responsible for the cracks in LPBF of molybdenum regardless of the processing temperature. Alloying molybdenum with 0.45 wt.% carbon diminishes the detrimental effects of oxygen by three effects: Firstly outgassing of carbon monoxide, secondly by increasing the grain boundary surface through constitutional undercooling and thirdly by trapping the oxygen within the carbide which has good coherency to the molybdenum matrix. The hardening effects of the finely dispersed carbide network must be overcome by building temperatures of 800 °C and higher to prevent cold cracking. The herein presented alloying and processing strategies enable molybdenum to be manufactured in LPBF free of cracks.