  Let $\C$ be a triangulated category with a cluster tilting subcategory $\T$.
We introduce the notion of $\T[1]$-cluster tilting subcategories (also called
ghost cluster tilting subcategories) of $\C$, which are a generalization of
cluster tilting subcategories. We first develop a basic theory on ghost cluster
tilting subcategories. Secondly, we study links between ghost cluster tilting
theory and $\tau$-tilting theory: Inspired by the work of Iyama, J{\o}rgensen
and Yang \cite{ijy}, we introduce the notion of $\tau$-tilting subcategories
and tilting subcategories of $\mod\T$. We show that there exists a bijection
between weak $\T[1]$-cluster tilting subcategories of $\C$ and support
$\tau$-tilting subcategories of $\mod\T$. Moreover, we figure out the
subcategories of $\mod\T$ which correspond to cluster tilting subcategories of
$\C$. This generalizes and improves several results by Adachi-Iyama-Reiten
\cite{AIR}, Beligiannis \cite{Be2}, and Yang-Zhu \cite{YZ}. Finally, we prove
that the definition of ghost cluster tilting objects is equivalent to the
definition of relative cluster tilting objects introduced by the first and the
third author in \cite{YZ}.
