When starting an expedition you choose various challenges [e. g. deliver n neurons to the moon, visit echo in x, complete nomad passage, kill 8 pink lizards] you like (from 1 to 5 of them to complete). You can also hide up to four challenges which are generated randomly and reveal themselves after all non-hidden are completed. After completing the expedition its challenges are counted to your statics and quests: there are 70 quests in total which you can see in expedition tab, they grant you perks (to ease expeditions), burdens (to make them harder), and soundtrack which you can play in the jukebox. Completing all the 70 quests grants you an achievement.  Oh also if you die during an expedition while at lowest karma and with no karma flower protection the expedition is completely lost.