Different atomistic registry between the layers forming the inner and outer nanotubes can form one-dimensional (1D) van der Waals (vdW) moire superlattices. Unlike the two-dimensional (2D) vdW moire superlattices, effects of 1D vdW moire superlattices on electronic and optical properties in 1D moire superlattices are not well understood, and they are often neglected. In this Perspective, we summarize new experimental observations and theoretical perspectives related to interlayer interactions in double-walled carbon nanotubes (DWNTs), a representative 1D vdW moire system. Our discussion will focus on new optical features emerging from the interlayer electronic interactions in DWNTs. Exciting correlated physics and exotic phases of matter are anticipated to exist in 1D vdW moire superlattices, analogous with those discovered in the 2D vdW moire superlattices. We further discuss the future directions in probing and uncovering interesting physical phenomena in 1D moire superlattices.