The most general two-Higgs-doublet model consists of two indistinguishable hypercharge-one complex scalar doublets. Consequently, physical quantities must be independent of the basis choice of the two scalar fields. As an example, the ratio of vacuum expectation values depends on the choice of basis and is hence unphysical. In this talk, a basis-independent formalism is introduced which allows one to directly identify the physical observables of the theory. As an example of this formalism, the necessary and sufficient condi-tions for an explicitly CP-violating scalar sector are determined. These conditions are highly non-trivial and can be expressed in terms of four independent invariants that depend on the Higgs potential parameters.