Caching popular contents in advance is an important technique to achieve the low latency requirement and to reduce the backhaul costs in future wireless communications. Considering a network with base stations distributed as a Poisson point process (PPP), optimal content placement caching probabilities are derived for known popularity profile, which is unknown in practice. In this paper, online prediction (OP) and online learning (OL) methods are presented based on popularity prediction model (PPM) and Grassmannian prediction model (GPM), to predict the content profile for future time slots for time-varying popularities. In OP, the problem of finding the coefficients is modeled as a constrained non-negative least squares (NNLS) problem which is solved with a modified NNLS algorithm. In addition, these two models are compared with log-request prediction model (RPM), information prediction model (IPM) and average success probability (ASP) based model. Next, in OL methods for the time-varying case, the cumulative mean squared error (MSE) is minimized and the MSE regret is analyzed for each of the models. Moreover, for quasi-time varying case where the popularity changes block-wise, KWIK (know what it knows) learning method is modified for these models to improve the prediction MSE and ASP performance. Simulation results show that for OP, PPM and GPM provides the best ASP among these models, concluding that minimum mean squared error based models do not necessarily result in optimal ASP. OL based models yield approximately similar ASP and MSE, while for quasi-time varying case, KWIK methods provide better performance, which has been verified with MovieLens dataset.