Cascades　are　ubiquitous　in　various　network　environments.　Predicting　these　cascades　is　decidedly　nontrivial　in　various　important　applications,　such　as　viral　marketing,　epidemic　prevention,　and　traffic　management.　Most　previous　works　have　focused　on　predicting　the　final　cascade　sizes.　As　cascades　are　dynamic　processes,　it　is　always　interesting　and　important　to　predict　the　cascade　size　at　any　given　time,　or　to　predict　the　time　when　a　cascade　will　reach　a　certain　size　(e.g.,　the　threshold　for　an　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,　can　we　predict　its　cumulative　cascade　size　at　any　later　time?　For　such　a　challenging　problem,　an　understanding　of　the　micromechanism　that　drives　and　generates　the　macrophenomena　(i.e.,　the　cascading　process)　is　essential.　Here,　we　introduce　behavioral　dynamics　as　the　micromechanism　to　describe　the　dynamic　process　of　an　infected　node＇s　neighbors　getting　infected　by　a　cascade　(i.e.,　one-hop　sub-cascades).　Through　data-driven　analysis,　we　find　out　the　common　principles　and　patterns　lying　in　the　behavioral　dynamics　and　propose　the　novel　NEtworked　WEibull　Regression　model　for　modeling　it.　We　also　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　evaluate　the　proposed　method　extensively　on　a　large-scale　social　network　dataset.　The　results　demonstrate　that　the　proposed　method　can　significantly　outperform　other　state-of-the-art　methods　in　multiple　tasks　including　cascade　size　prediction,　outbreak　time　prediction,　and　cascading　process　prediction.