Molecular wires (MW) are the fundamental building blocks for molecular electronic devices. They consist of a molecular unit connected to two continuum reservoirs of electrons (usually metallic leads). We rely on Landauer theory as the basis for studying the conductance properties of MW systems. This relates the lead to lead current to the transmission probability for an electron to scatter through the molecule. Two different methods have been developed for the study of this scattering. One is based on a solution of the Lippmann-Schwinger equation and the other solves for the t matrix using Schroedinger's equation. We use our methodology to study two problems of current interest. The first MW system consists of 1,4 benzene-dithiolate (BDT) bonded to two gold nanocontacts. Our calculations show that the conductance is sensitive to the chemical bonding between the molecule and the leads. The second system we study highlights the interesting phenomenon of antiresonances in MW. We derive an analytic formula predicting at what energies antiresonances should occur in the transmission spectra of MW. A numerical calculation for a MW consisting of filter molecules attached to an active molecule shows the existence of an antiresonance at the energy predicted by our formula.