Portable and inexpensive gas sensors are essential for the next generation of non-invasive medical diagnostics, smart air quality monitoring & control, human search & rescue and food quality assessment to name a few of their immediate applications. Therein, analyte selectivity in complex gas mixtures like breath or indoor air remains the major challenge. Filters are an effective and versatile, though often unrecognized, route to overcome selectivity issues by exploiting additional properties of target analytes (e.g., molecular size and surface affinity) besides reactivity with the sensing material. This review provides a tutorial for the material engineering of sorption, size-selective and catalytic filters. Of specific interest are high surface area sorbents (e.g., activated carbon, silica gels and porous polymers) with tunable properties, microporous materials (e.g., zeolites and metal-organic frameworks) and heterogeneous catalysts, respectively. Emphasis is placed on material design for targeted gas separation, portable device integration and performance. Finally, research frontiers and opportunities for low-cost gas sensing systems in emerging applications are highlighted.