The James Webb Space Telescope near-infrared camera (JWST NIRCam) has two 2.02 x 2.02 fields of view that are capable of either imaging or spectroscopic observations. Either of two R ∼ 1500 grisms with orthogonal dispersion directions can be used for slitless spectroscopy over λ = 2.4 - 5.0 μm in each module, and shorter wavelength observations of the same fields can be obtained simultaneously. We present the latest predicted grism sensitivities, saturation limits, resolving power, and wavelength coverage values based on component measurements, instrument tests, and end-to-end modeling. Short wavelength (0.6 - 2.3 μm) imaging observations of the 2.4 - 5.0 μm spectroscopic field can be performed in one of several different filter bands, either in-focus or defocused via weak lenses internal to NIRCam. Alternatively, the possibility of 1.0 - 2.0 μm spectroscopy (simultaneously with 2.4 - 5.0 μm) using dispersed Hartmann sensors (DHSs) is being explored. The grisms, weak lenses, and DHS elements were included in NIRCam primarily for wavefront sensing purposes, but all have significant science applications. Operational considerations including subarray sizes, and data volume limits are also discussed. Finally, we describe spectral simulation tools and illustrate potential scientific uses of the grisms by presenting simulated observations of deep extragalactic fields, galactic dark clouds, and transiting exoplanets.