Implicit numerical methods such as the stochastic theta-method offer a practical way to approximate solutions of stochastic differential equations. The method involves a parameter, θ, which is freely chosen. In this thesis, we investigate strong convergence and linear stability, both mean-square and asymptotic, arising from the implementation of the theta-method when applied to ordinary stochastic differential equations incoroporating jumps. Such models are used in several disciplines; in particular, we note their use as models for various financial quantities such as asset prices, interest rates and volatility.