SpaceX IS the newcomer and underdog, but one that's advancing very quickly. The big monopolist in this case is ULA, the "United Launch Alliance", which was created in 2006 as a joint venture of Lockheed Martin Space Systems and Boeing Defense, Space & Security.
For years, ULA was only option for US government launch contracts. They had more than 100 launches – all of them successful except one single minor anomaly [1].
SpaceX tried and succeeded [2] to get into the lucrative government contract business, arguing that their launches are five times cheaper (90M vs 460M USD).
Before that, an interesting meeting of the U.S. Committee on Armed Services took place [3], discussing ULA's dependency on russian-made RD-180 rocket engines for their Atlas V launch system.
[1] http://www.spacepolicyonline.com/news/ula-traces-atlas-v-ano...
[2] https://spaceflightnow.com/2015/05/27/spacex-cleared-to-laun...