MO recognizes CC licenses from all other 49 states.
Here's a link to the statute. Most of what you will need to know for CC is in 571.107.1: http://www.moga.mo.gov/statutes/chapters/chap571.htm
Note that in MO a CC permit/license is a CCW (concealed carry weapons) permit which exempts the licensee from the carry of dangerous weapons statute. The only thing you cannot carry concealed with a CCW in MO are switchblades and gravity knives such as a butterfly knife. Any other knife or even a machete, a collapsible baton or even long arms or shot guns can be carried concealed if so licensed from any state.
As to OC, that is an entirely different issue. We have no state preemption for OC and any municipality can make any ordinance prohibiting it. Counties cannot. If you are in an incorporated area, you must find out if that city has an ordinance prohibiting OC. In some areas where not illegal it is not uncommon and the LEO won't even blink, especially during hunting seasons, in other areas it is rarely seen and may lead to a discussion with LEO.
Here is a publication from the MSHP which gives a bit of a quick overview of CC laws and carry in cars. I used to have this printed out and in my vehicle until I realized that LEOs are aware of this info and the few who are not won't care: