In this survey, we give a neat summary of the applications of the multi-resolution analysis to the studies of Besov-Q type spaces {\dot{B}}_{p,q}^{{\gamma }_1,{\gamma }_2}({\text{ℝ}}^n) and Triebel-Lizorkin-Q type spaces {\dot{B}}_{p,q}^{{\gamma }_1,{\gamma }_2}({\text{ℝ}}^n). We will state briefly the recent progress on the wavelet characterizations, the boundedness of Calderón-Zygmund operators, the boundary value problem of {\dot{B}}_{p,q}^{{\gamma }_1,{\gamma }_2}({\text{ℝ}}^n) and {\dot{F}}_{p,q}^{{\gamma }_1,{\gamma }_2}({\text{ℝ}}^n). We also present the recent developments on the well-posedness of fluid equations with small data in {\dot{B}}_{p,q}^{{\gamma }_1,{\gamma }_2}({\text{ℝ}}^n) and {\dot{F}}_{p,q}^{{\gamma }_1,{\gamma }_2}({\text{ℝ}}^n).