Cascades are ubiquitous in various network environments. How to predict these cascades is highly nontrivial in several vital applications, such as viral marketing, epidemic prevention and traffic management. Most previous works mainly focus on predicting the final cascade sizes. As cascades are typical dynamic processes, it is always interesting and important to predict the cascade size at any time, or predict the time when a cascade will reach a certain size (e.g. an threshold for outbreak). In this paper, we unify all these tasks into a fundamental problem: cascading process prediction. That is, given the early stage of a cascade, how to predict its cumulative cascade size of any later time? For such a challenging problem, how to understand the micro mechanism that drives and generates the macro phenomena (i.e. cascading process) is essential. Here we introduce behavioral dynamics as the micro mechanism to describe the dynamic process of a node's neighbors getting infected by a cascade after this node getting infected (i.e. one-hop subcascades). Through data-driven analysis, we find out the common principles and patterns lying in behavioral dynamics and propose a novel Networked Weibull Regression model for behavioral dynamics modeling. After that we propose a novel method for predicting cascading processes by effectively aggregating behavioral dynamics, and present a scalable solution to approximate the cascading process with a theoretical guarantee. We extensively evaluate the proposed method on a large scale social network dataset. The results demonstrate that the proposed method can significantly outperform other state-of-the-art baselines in multiple tasks including cascade size prediction, outbreak time prediction and cascading process prediction.