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The Swedish national height system is called RH 2000 and was officially adopted in 2005. There are also older national height systems as well as a large number of local heights systems.
National height systems
The height system RH 2000 is based on the third precision levelling campaign.
RH 70 is the previous national height system, that was formally superseded by RH 2000 in 2005.
RHB 70 is not a height system in proper meaning, but rather a densification and, to a certain extent, a re-measurement of RH 70. RHB 70 is based on levelling data of high quality from the third precise levelling campaign.
RH 00 was used for a long time on the local level, but was obsolete on the national level already long ago.
Local height systems
A large number of local height systems have been used in the municipalities. RH 00 often was the origin of those. However, because of the insufficient quality of RH 00 such local height systems often must be referred to as entirely local.