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Citywide crowd flow analytics is of great importance to smart city efforts. It aims to model the crowd flow (e.g., inflow and outflow) of each region in a city based on historical observations. Nowadays, Convolutional Neural Networks (CNNs) have been widely adopted in raster-based crowd flow analytics by virtue of their capability in capturing spatial dependencies. After revisiting CNN-based methods for different analytics tasks, we expose two common critical drawbacks in the existing uses: 1) inefficiency in learning global spatial dependencies, and 2) overlooking latent region functions. To tackle these challenges, in this paper we present a novel framework entitled DeepLGR that can be easily generalized to address various citywide crowd flow analytics problems. This framework consists of three parts: 1) a local feature extraction module to learn representations for each region; 2) a global context module to extract global contextual priors and upsample them to generate the global features; and 3) a region-specific predictor based on tensor decomposition to provide customized predictions for each region, which is very parameter-efficient compared to previous methods. Extensive experiments on two typical crowd flow analytics tasks demonstrate the effectiveness, stability, and generality of our framework.