Given one or more query vertices, Community Search (CS) aims to find densely intra-connected and loosely inter-connected structures containing query vertices. Attributed Community Search (ACS), a related problem, is more challenging since it finds communities with both cohesive structures and homogeneous vertex attributes. However, most methods for the CS task rely on inflexible pre-defined structures and studies for ACS treat each attribute independently. Moreover, the most popular ACS strategies decompose ACS into two separate sub-problems, i.e., the CS task and subsequent attribute filtering task. However, in real-world graphs, the community structure and the vertex attributes are closely correlated to each other. This correlation is vital for the ACS problem. In this paper, we propose Graph Neural Network models for both CS and ACS problems, i.e., Query Driven-GNN and Attributed Query Driven-GNN. In QD-GNN, we combine the local query-dependent structure and global graph embedding. In order to extend QD-GNN to handle attributes, we model vertex attributes as a bipartite graph and capture the relation between attributes by constructing GNNs on this bipartite graph. With a Feature Fusion operator, AQD-GNN processes the structure and attribute simultaneously and predicts communities according to each attributed query. Experiments on real-world graphs with ground-truth communities demonstrate that the proposed models outperform existing CS and ACS algorithms in terms of both efficiency and effectiveness. More recently, an interactive setting for CS is proposed that allows users to adjust the predicted communities. We further verify our approaches under the interactive setting and extend to the attributed context. Our method achieves 2.37% and 6.29% improvements in F1-score than the state-of-the-art model without attributes and with attributes respectively.