  The main purpose of this paper is to investigate characterizations of
composition operators on Bloch and Hardy type spaces. Initially, we use general
doubling weights to study the composition operators from
  harmonic Bloch type spaces on the unit disc $\mathbb{D}$
  to pluriharmonic Hardy spaces on the Euclidean unit ball $\mathbb{B}^n$.
Furthermore, we develop some new methods to study the composition operators
from harmonic Bloch type spaces on $\mathbb{D}$ to pluriharmonic Bloch type
spaces on $\mathbb{D}$.
  Additionally, some application to new characterizations of the composition
operators between pluriharmonic Lipschitz type spaces to be bounded or compact
will be presented. The obtained results of this paper provide the improvements
and extensions of the corresponding known results.
