We demonstrate a paper-based surface swab and lateral-flow dipstick that includes an inkjet-printed surface-enhanced Raman spectroscopy (SERS) substrate for analyte detection. Due to capillary-action wicking of cellulose, the paper dipstick enables extremely simple and pump-free loading of liquid samples into the detection device, and in addition provides inherent analyte concentration within the detection volume. Furthermore, the flexible nature of the paper-based SERS device also enables it to act as a swab to collect analyte molecules directly from a large-area surface; the collected analyte molecules can then be focused into a small-volume SERS-active region by lateral-flow concentration. These capabilities are unseen in today's SERS substrates and microfluidic SERS devices. Using these novel lateral-flow paper SERS devices, we achieved detection limits as low as 95 fg of Rhodamine 6G (R6G), 413 pg of the organophosphate malathion, 9 ng of heroin, and 15 ng of cocaine. Moreover, the measurements show that the technique is quantitative and is repeatable across multiple swabs and dipsticks. The results reported here may lead to ultra-low-cost portable applications in trace chemical detection.