Cancer metastasis accounts for the majority of cancer-related deaths owing to poor response to anticancer therapies. Molecular understanding of metastasis-associated drug resistance remains elusive due to the scarcity of available tumor tissue. Isolation of circulating tumor cells (CTCs) from the peripheral blood of patients has emerged as a valid alternative source of tumor tissue that can be subjected to molecular characterization. However, issues with low purity and sensitivity have impeded adoption to clinical practice. Here we report a novel method to capture and molecularly characterize CTCs isolated from castrate-resistant prostate cancer patients (CRPC) receiving taxane chemotherapy. We have developed a geometrically enhanced differential immunocapture (GEDI) microfluidic device that combines an anti-prostate specific membrane antigen (PSMA) antibody with a 3D geometry that captures CTCs while minimizing nonspecific leukocyte adhesion. Enumeration of GEDI-captured CTCs (defined as intact, nucleated PSMA+/CD45- cells) revealed a median of 54 cells per ml identified in CRPC patients versus 3 in healthy donors. Direct comparison with the commercially available CellSearch® revealed a 2-400 fold higher sensitivity achieved with the GEDI device. Confocal microscopy of patient-derived GEDI-captured CTCs identified the TMPRSS2:ERG fusion protein, while sequencing identified specific androgen receptor point mutation (T868A) in blood samples spiked with only 50 PC C4-2 cells. On-chip treatment of patient-derived CTCs with docetaxel and paclitaxel allowed monitoring of drug-target engagement by means of microtubule bundling. CTCs isolated from docetaxel-resistant CRPC patients did not show any evidence of drug activity. These measurements constitute the first functional assays of drug-target engagement in living circulating tumor cells and therefore have the potential to enable longitudinal monitoring of target response and inform the development of new anticancer agents.