Despite the ubiquity of physical obstacles (e.g., buildings, hills, and blindages, etc.) in the real world, most of spatial queries ignore the obstacles. In this article, we study a novel form of continuous nearest-neighbor queries in the presence of obstacles, namely continuous obstructed nearest-neighbor (CONN) search, which considers the impact of obstacles on the distance between objects. Given a data set P , an obstacle set O , and a query line segment q , in a two-dimensional space, a CONN query retrieves the nearest neighbor p ∈ P of each point p′ on q according to the obstructed distance, the shortest path between p and p ′ without crossing any obstacle in O . We formalize CONN search, analyze its unique properties, and develop algorithms for exact CONN query-processing assuming that both P and O are indexed by conventional data-partitioning indices (e.g., R-trees). Our methods tackle CONN retrieval by performing a single query for the entire query line segment, and only process the data points and obstacles relevant to the final query result via a novel concept of control points and an efficient quadratic-based split point computation approach. Then, we extend our techniques to handle variations of CONN queries, including (1) continuous obstructed k nearest neighbor (CO k NN) search which, based on obstructed distances, finds the k (≥ 1) nearest neighbors (NNs) to every point along q ; and (2) trajectory obstructed k nearest-neighbor (TO k NN) search, which, according to obstructed distances, returns the k NNs for each point on an arbitrary trajectory (consisting of several consecutive line segments). Finally, we explore approximate CO k NN (ACO k NN) retrieval. Extensive experiments with both real and synthetic datasets demonstrate the efficiency and effectiveness of our proposed algorithms under various experimental settings.