Bags or liners having incorporated therein an effective amount of odor management agents including a counteractant agent, a neutralizing agent and optionally, a masking agent, whereby the odor management agent imparts no perceptible scent to the bags or liners, such that the bags or liners are substantially free of fragrance while the odor management agent reduces malodor emanating from products disposed within the bag. Further, the invention is drawn to web materials for use in forming the bags or liners having odor management agents. The odor management agent is disposed within the bag or dispersed substantially uniformly throughout the web.