Given analytic function spaces \(X\) and \(Y\) on the unit disk in the complex plane, let \(M(X, Y)\) be the space of all analytic pointwise multipliers from \(X\) into \(Y\). In this paper, the author provides characterizations of \(M(X, Y)\) for two cases. One is the case where \(X\) is a weighted Bergman space and \(Y\) is another weighted Bergman space. The other is the case where \(X\) is a Hardy space and \(Y\) is a weighted Bergman space. These results generalize earlier works of \textit{K. R. M. Attele} [Mich. Math. J. 31, 307--319 (1984; Zbl 0589.46042)] and \textit{N. S. Feldman} [Ill. J. Math. 43, 211--221 (1999; Zbl 0936.30038)]. The characterizations are complete in the sense that the full range of parameters is covered. The characterizations are given in terms of well-known function spaces such as Bloch type spaces, BMOA type spaces, weighted Bergman spaces and tent spaces.