In this thesis we examine the ability of the log-periodic power law model to accurately predict the end of speculative bubbles on financial markets through modeling of asset price dynamics on a selection of historical bubbles. The methods we use are based on a nonlinear least squares estimation which yields predictions of when the bubble will change regime.We find evidence which support the occurrence of LPPL-patterns leading up to the change in regime; asset prices during bubble periods seem to oscillate around a faster-than-exponential growth. In most cases the estimation yields accurate predictions, although we conclude that the predictions are quite dependent on at which point in time the prediction is conducted. We also find that the end of a speculative bubble seems to be influenced by both endogenous speculative growth and exogenous factors. For this reason we propose a new way of interpreting the predictions of the model, where the end dates should be interpreted as the start of a time period where the asset prices are especially sensitive to exogenous events. We propose that negative news during this time period results in a regime shift of the bubble. This study is the first to address both the possibilities and the limitations of the LPPL-model, and should therefore be considered as a contribution to the academia.