We address challenges and opportunities presented by the emerging paradigm of sensing spatial fields using moving sensors. - We design sensor trajectories that have low path density, i.e., the distance traveled by the mobile sensors per unit area. We obtain fundamental limits on the path density for a mobile sensing scheme that admits stable sampling and reconstruction of a bandlimited spatial field - We show that mobile sensors can perform spatial anti-aliasing filtering - We identify the optimal method to match a set of unlabeled statistics to an independent set of labeled observations. We show that anonymized time-averaged mobility statistics of a set of users can be easily de-anonymized using auxiliary information. Thus privacy offered by anonymization and averaging is insufficient