Humans use abstract concepts for understanding instead of hard features. Recent interpretability research has focused on human-centered concept explanations of neural networks. Concept Activation Vectors (CAVs) estimate a model's sensitivity and possible biases to a given concept. We extend CAVs from post-hoc analysis to ante-hoc training to reduce model bias through fine-tuning using an additional Concept Loss. Concepts are defined on the final layer of the network in the past. We generalize it to intermediate layers, including the last convolution layer. We also introduce Concept Distillation, a method to define rich and effective concepts using a pre-trained knowledgeable model as the teacher. Our method can sensitize or desensitize a model towards concepts. We show applications of concept-sensitive training to debias several classification problems. We also show a way to induce prior knowledge into a reconstruction problem. We show that concept-sensitive training can improve model interpretability, reduce biases, and induce prior knowledge.