Estimating wildlife abundance is fundamental for its effective management and conservation. A range of methods exist: total counts, plot sampling, distance sampling and capture-recapture based approaches. Methods have assumptions and their failure can lead to substantial bias. Current research in the field is focused not on establishing new methods but in extending existing methods to deal with their assumptions' violation. This thesis focus on incorporating animal movement into circular plot sampling (CPS) and point transect sampling (PTS), where a key assumption is that animals do not move while within detection range, i.e., the survey is a snapshot in time. While targeting this goal, we found some unexpected bias in PTS when animals were still and model selection was used to choose among different candidate models for the detection function (the model describing how detectability changes with observer-animal distance). Using a simulation study, we found that, although PTS estimators are asymptotically unbiased, for the recommended sample sizes the bias depended on the form of the true detection function. We then extended the simulation study to include animal movement, and found this led to further bias in CPS and PTS. We present novel methods that incorporate animal movement with constant speed into estimates of abundance. First, in CPS, we present an analytic expression to correct for the bias given linear movement. When movement is de ned by a diffusion process, a simulation based approach, modelling the probability of animal presence in the circular plot, results in less than 3% bias in the abundance estimates. For PTS we introduce an estimator composed of two linked submodels: the movement (animals moving linearly) and the detection model. The performance of the proposed method is assessed via simulation. Despite being biased, the new estimator yields improved results compared to ignoring animal movement using conventional PTS.