This is a joint work with Benjamin Espinoza, Alejandro Illanes, Hayato Imamura and Yoshiyuki Oshima. In this presentation, we discuss some recent results on decomposable continua, in particular, Wilder continua, continuum-wise Wilder continua, closed set-wise Wilder continua, $D$-continua, $D^{\ast }$-continua and $D^{\ast \ast }$. First, we introduce some basic definitions and terminology that are used in this talk. Then, we discuss results on the above continua related to Whitney properties and Whitney reversible properties. Also, we deal with product properties as for those continua. Finally, we show the existence of singular decomposable continua using those notion.