We present the results of radio continuum (20 and 6 cm) and optical emission-line (H-alpha + [N II] lambda-lambda-6548, 6584 and [O III] lambda-5007) imaging observations of the type 1 Seyfert galaxy NGC 3516. These observations were obtained with the VLA and the William Herschel Telescope and are deeper and of higher resolution than earlier ones. The radio maps reveal an elongated, one-sided, curved structure, which comprises a series of small-scale "blobs" and extends up to 4 kpc from the nucleus. This radio structure is aligned and cospatial with one side of the double-sided and highly symmetric Z-shaped emission-line structure. We argue that these morphological features are associated with a bipolar, gaseous outflow from the nucleus of NGC 3516. The radio "blobs" are elongated roughly perpendicular to the apparent local direction of the outflow, a result which we interpret in terms of synchrotron emission from outflow-driven shock waves. For one such "blob," the associated optical emission-line feature is displaced slightly toward the nucleus, suggesting that the line emission originates in the postshock cooling zone. There is an approximate equality between relativistic and thermal pressures in much of the nebulosity. The apparent bending of the outflow may reflect either collision with the rotating interstellar gas, or gravitationally induced trajectories in a low-velocity outflow, or precession of the nuclear axis. The direction of the present axis of the putative collimating nuclear disk is indicated by both the extended radio continuum and line emission on the smallest resolved scales (400 pc), and by the optical continuum polarization of the nucleus. Last, we note a very elongated emission-line feature about 3.3 kpc from the nucleus, that "points" toward the nucleus and is well aligned with the present nuclear axis. It is suggested that this feature represents ambient interstellar gas photoionized by a narrow beam of radiation ("blazar-like"?) from the nucleus. Such emission-line structures may be useful probes of "blazars" when the jet is not directed toward Earth.