At an Anderson transition wavefunctions undergo large amplitude
fluctuations. The corresponding amplitude moments show a power law
scaling with the sample size introducing a set of exponents, the
"multifractality spectrum". This spectrum is a unique und universal
characteristics of the transition. Recent work has shown, that the
critical wavefunctions have a different amplitude distribution near
surfaces giving rise to a second set of exponents, the
"surface multifractality" spectrum. The talk offers an introduction into
the topic and an overview about recent developments.