Deep Neural Networks (DNNs) have advanced the state-of-the-art in a variety of machine learning tasks and are deployed in increasing numbers of products and services. However, the computational requirements of training and evaluating large-scale DNNs are growing at a much faster pace than the capabilities of the underlying hardware platforms that they are executed upon. In this work, we propose Dynamic Variable Effort Deep Neural Networks (DyVEDeep) to reduce the computational requirements of DNNs during inference. Previous efforts propose specialized hardware implementations for DNNs, statically prune the network, or compress the weights. Complementary to these approaches, DyVEDeep is a dynamic approach that exploits the heterogeneity in the inputs to DNNs to improve their compute efficiency with comparable classification accuracy. DyVEDeep equips DNNs with dynamic effort mechanisms that, in the course of processing an input, identify how critical a group of computations are to classify the input. DyVEDeep dynamically focuses its compute effort only on the critical computa- tions, while skipping or approximating the rest. We propose 3 effort knobs that operate at different levels of granularity viz. neuron, feature and layer levels. We build DyVEDeep versions for 5 popular image recognition benchmarks - one for CIFAR-10 and four for ImageNet (AlexNet, OverFeat and VGG-16, weight-compressed AlexNet). Across all benchmarks, DyVEDeep achieves 2.1x-2.6x reduction in the number of scalar operations, which translates to 1.8x-2.3x performance improvement over a Caffe-based implementation, with < 0.5% loss in accuracy.