Data referring to cultural calendars such as the widespread Gregorian dates but also dates after the Chinese, Hebrew, or Islamic calendars as well as data referring to professional calendars like fiscal years or teaching terms are omnipresent on the Web. Formalisms such as XML Schema have acknowledged this by offering a rather extensive set of Gregorian dates and times as basic data types. This article introduces into CaTTS, the Calendar and Time Type System. CaTTS goes far beyond predefined date and time types after the Gregorian calendar as supported by XML Schema. CaTTS first gives rise to declaratively specify more or less complex cultural or professional calendars including specificities such as leap seconds, leap years, and time zones. CaTTS further offers a tool for the static type checking (of data typed after calendar(s) defined in CaTTS). CaTTS finally offers a language for declaratively expressing and a solver for efficiently solving temporal constraints (referring to calendar(s) expressed in CaTTS). CaTTS complements data modeling and reasoning methods designed for generic Semantic Web applications such as RDF or OWL with methods specific to the particular application domain of calendars and time.