Let $(X, d, \mu )$ be a metric space with a metric $d$ and a doubling measure $\mu$.  Assume that the operator $L$ generates a bounded holomorphic semigroup $e^{-tL}$ on $L^2(X)$ whose semigroup kernel satisfies the Gaussian upper bound. Also assume that $L$ has bounded holomorphic functional calculus on $L^2(X)$. Then  the Hardy spaces  $H^p_L(X)$ associated with the operator $L$ can be defined for $0 < p \le 1$. In this talk, we revisit the Calder\'on-Zygmund decomposition and show that a function $f \in L^1(X)\cap L^2(X)$ can be decomposed into a good part and a bad part which is in $H^p_L(X)$ for some $0 < p <1$. An important result of our variants of Calder\'on-Zygmund decompositions is that if a sub-linear operator $T$ is bounded from $L^r(X)$ to $L^r(X)$ for some $r > 1$ and also bounded from $H^p_L(X)$ to $L^p(X)$ for some $0 <  p < 1$, then $T$ is of weak type $(1,1)$ and bounded from $L^q(X)$ to $L^q(X)$ for all $1< q <r$.