Accepted for publication in the A&A Herschel Special IssueLocal luminosity functions are fundamental benchmarks for high-redshift galaxy formation and evolution studies as well as for models describing these processes. Determining the local luminosity function in the submillimeter range can help to better constrain in particular the bolometric luminosity density in the local Universe, and Herschel offers the first opportunity to do so in an unbiased way by imaging large sky areas at several submillimeter wavelengths. We present the first Herschel measurement of the submillimeter