Non-3GPP Access technologies such as WLAN technologies can be connected to the 3GPP core network like EPC (Evolved Packet Core) in various ways based on the operator’s business models and architectural preferences. The desire to provide this access to the 5G core network, currently defined in 3GPP, requires the design of new protocols and procedures in order to fulfill all requirements. This paper describes the current status of the specification in Release 15 of the untrusted non-3GPP access where the mobile operator does not trust the access point and tunnels all traffic to a trusted gateway in the mobile network. Further, the paper provides an outlook of the new Release 16 feature for trusted non-3GPP access, i.e. the mobile operator trusts the access point, as well as the feature for 5G core network access from WLAN devices with 3GPP credentials that do not support the Non Access Stratum protocol.