Bound states in the continuum (BICs) are radiationless localized states embedded in the part of the parameter space that otherwise corresponds to radiative modes. Many decades after their original prediction and early observations in acoustic systems, such states have been demonstrated recently in photonic structures with engineered geometries. Here, we put forward a mechanism, based on waveguiding structures that contain anisotropic birefringent materials, that affords the existence of BICs with fundamentally new properties. In particular, anisotropy-induced BICs may exist in symmetric as well as in asymmetric geometries; they form in tunable angular propagation directions; their polarization may be pure transverse electric, pure transverse magnetic or full vector with tunable polarization hybridity; and they may be the only possible bound states of properly designed structures, and thus appear as a discrete, isolated bound state embedded in a whole sea of radiative states.
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