Wormholes are bridges connecting two regions of spacetime. These regions may be considered in a universe or two different universes. These geometries are solutions to the equations of gravitational theories, such as Einstein’s general relativity. In this thesis, we examine the behavior of the classical scalar and Maxwell fields in the background of static and spherically symmetric wormholes, and show that certain geometric properties of such wormholes can be studied by examining the asymptotic behavior of the fields. We show that the scalar field equation can be analyzed by using the spherical symmetry and the method of separation of variables to separate the contribution of the angular momentumterm, and converting the radial equation to the Schr?dinger equation, reducing it to the scattering problem in one-dimensional quantum mechanics, and calculating the potential function corresponding to every wormhole. This potential function, in addition to a general contribution from the angular momentum, also depends on the peculiarities of the geometry. By calculating the scattering matrix, we obtain the transmission and reflection amplitudes for the scalar field scattered by the wormhole. For classical Maxwell fields, by extending the concepts of electric and magnetic fields from Minkowski spacetime to the wormhole spacetime, we show that the optical characteristics of wormholes can be simulated by interpreting the curvature effects of the spacetime in terms of the permittivity and permeability of a certain optical medium in the flat spacetime. Given the asymptotic behavior of this geometry, which is similar to the flat spacetime, we write the solution in terms of the multipole expansion and show that the correct variable of this series is not the ordinary radial coordinate, but a definite function thereof. We show that this specific change of variable actually represents the symmetry of the Maxwell equations under the conformal transformations of the metric. Since the Maxwell action is invariant under the conformal transformations of the spacetime metric, instead of solving the Maxwell equations in some given geometry, we can search for a solution in a simpler geometry obtained by conformal transformation. We approve the former results in this way. Keywords: wormholes, classical scalar field, classical Maxwell field, scattering in curved spacetime