We extend existing oceanographic sampling methodologies to sample an advecting feature of interest using autonomous robotic platforms. GPS-tracked Lagrangian drifters are used to tag and track a water patch of interest with position updates provided periodically to an autonomous underwater vehicle (AUV) for surveys around the drifter as it moves with ocean currents. Autonomous sampling methods currently rely on geographic waypoint track-line surveys that are suitable for static or slowly changing features. When studying dynamic, rapidly evolving oceanographic features, such methods at best introduce error through insufficient spatial and temporal resolution, and at worst, completely miss the spatial and temporal domain of interest. We demonstrate two approaches for tracking and sampling of advecting oceanographic features. The first relies on extending static-plan AUV surveys (the current state-of-the-art) to sample advecting features. The second approach involves planning of surveys in the drifter or patch frame of reference. We derive a quantitative envelope on patch speeds that can be tracked autonomously by AUVs and drifters and show results from a multi-day off-shore field trial. The results from the trial demonstrate the applicability of our approach to long-term tracking and sampling of advecting features. Additionally, we analyze the data from the trial to identify the sources of error that affect the quality of the surveys carried out. Our work presents the first set of experiments to autonomously observe advecting oceanographic features in the open ocean.