Constructing compact and informative 3D scene representations is essential for effective embodied exploration and reasoning, especially in complex environments over long periods. Existing scene representations, such as object-centric 3D scene graphs, have significant limitations. They oversimplify spatial relationships by modeling scenes as individual objects, with inter-object relationships described by restrictive texts, making it difficult to answer queries that require nuanced spatial understanding. Furthermore, these representations lack natural mechanisms for active exploration and memory management, which hampers their application to lifelong autonomy. In this work, we propose SnapMem, a novel snapshot-based scene representation serving as 3D scene memory for embodied agents. SnapMem employs informative images, termed Memory Snapshots, to capture rich visual information of explored regions. It also integrates frontier-based exploration by introducing Frontier Snapshots-glimpses of unexplored areas-that enable agents to make informed exploration decisions by considering both known and potential new information. Meanwhile, to support lifelong memory in active exploration settings, we further present an incremental construction pipeline for SnapMem, as well as an effective memory retrieval technique for memory management. Experimental results on three benchmarks demonstrate that SnapMem significantly enhances agents' exploration and reasoning capabilities in 3D environments over extended periods, highlighting its potential for advancing applications in embodied AI.