This thesis presents four self-contained empirical research papers on monetary policy and monetary transmission using vector autoregression (VAR), structural VAR (SVAR), and Bayesian time-varying parameter VAR (TVP-VAR) models. The first two papers compare aspects of monetary policy and transmission in selected developed countries: Australia, the US, and the Euro area (Chapter 3); and Australia, the US, UK, and Canada (Chapter 4). The last two papers (Chapters 5 and 6) explore monetary policy and effects of monetary policy on inflation in Vietnam - a transition developing country. The empirical results indicate that the investment channel of monetary policy transmission plays a more important role than the consumption channel in Australia. Meanwhile the investment channel and the consumption channel make similar contributions to the overall transmission of monetary policy in the Euro area and the US. The difference between Australia and the Euro area appears to come from differences in housing investment responses, whereas Australia differs from the US mainly because it has a lower share of household consumption in total demand. Results from TVP-VAR models suggest that there were comovements in the monetary policy reactions to unemployment across countries before the recent Global Financial Crisis (GFC). The policy rate seems to react more strongly to unemployment changes in more recent years, especially in the US and UK. Monetary policy responses to inflation/deflation are observed to be divided into two groups, with the responses in the US and UK showing a different pattern to the responses in Canada and Australia. Monetary policy seems to react most aggressively against inflation/deflation in the US. The effects of monetary policy shocks on unemployment and inflation are similar across countries, and seem to have weakened over time. Results also suggest that monetary policy transmission to inflation in a transition country like Vietnam appears to work in a similar way to as in developed countries. The impulse response functions of inflation to shocks in monetary policy are plausible and robust across the VAR and SVAR models. The policy interest rate plays an important role in affecting inflation. For the case of Vietnam as a small, open economy, shocks to output and prices in trading partners also appear to have strong effects on domestic inflation. Allowing for the time-varying nature of the parameters and variance/covariance matrices, the results suggest that the State Bank of Vietnam (SBV) appears to have been steadily using monetary policy tools to contain inflation. TVP-VAR results also confirm that monetary policy in Vietnam appears to lead to reasonable inflation responses. The evidence therefore supports the argument that Vietnam's monetary policy might be more effective than expected.