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A number of observed phenomena associated with individual neutron starsystems or neutron star populations find explanations in models in which theneutron star crust plays an important role. We review recent work examining thesensitivity to the slope of the symmetry energy $L$ of such models, andconstraints extracted on $L$ from confronting them with observations. We focuson six sets of observations and proposed explanations: (i) The cooling rate ofthe neutron star in Cassiopeia A, confronting cooling models which includeenhanced cooling in the nuclear pasta regions of the inner crust, (ii) theupper limit of the observed periods of young X-ray pulsars, confronting modelsof magnetic field decay in the crust caused by the high resistivity of thenuclear pasta layer, (iii) glitches from the Vela pulsar, confronting theparadigm that they arise due to a sudden re-coupling of the crustal neutronsuperfluid to the crustal lattice after a period during which they weredecoupled due to vortex pinning, (iv) The frequencies of quasi-periodicoscillations in the X-ray tail of light curves from giant flares from softgamma-ray repeaters, confronting models of torsional crust oscillations, (v)the upper limit on the frequency to which millisecond pulsars can be spun-updue to accretion from a binary companion, confronting models of the r-modeinstability arising above a threshold frequency determined in part by theviscous dissipation timescale at the crust-core boundary, and (vi) theobservations of precursor electromagnetic flares a few seconds before shortgamma-ray bursts, confronting a model of crust shattering caused by resonantexcitation of a crustal oscillation mode by the tidal gravitational field of acompanion neutron star just before merger.

Constraints on the symmetry energy from observational probes of the neutron star crust