We discuss TMLE of target estimands for general longitudinal studies with time to event outcomes. In particular, we demonstrate a TMLE that targets a complete treatment specific survival function, thereby obtaining an efficient plug-in estimator of the treatment specific survival function that is a true survival function. We also discuss a new TMLE for the treatment specific survival function based on general longitudinal data structures with continuous monitoring. This TMLE can handle continuous time and random monitoring, contrary to the current sequential regression based TMLE based on the Bang and Robins (2005) representation. This TMLE uses a targeted maximum likelihood estimator of the intensities of the counting processes, while it uses a pooled regressions method to estimate the conditional means over the time-dependent covariates, given the past. Therefore, as with the sequential regression TMLE, this TMLE still avoids having to estimate the conditional density of the time-dependent covariate distribution, given the observed past. We demonstrate the methods with simulated and real data.