  The nuclear matter parameters define the nuclear equation of state (EoS),
they appear as coefficients of expansion around the saturation density of
symmetric and asymmetric nuclear matter. We review their correlations with
several properties of finite nuclei and of neutron stars within mean-field
frameworks. The lower order nuclear matter parameters such as the binding
energy per nucleon, incompressibility and the symmetry energy coefficients are
found to be constrained in narrow limits through their strong ties with
selective properties of finite nuclei. From the correlations of nuclear matter
parameters with neutron star observables, we further review how precision
knowledge of the radii and tidal deformability of neutron stars in the mass
range $1 - 2 M_\odot$ may help cast them in narrower bounds. The higher order
parameters such as the density slope and the curvature of the symmetry energy
or the skewness of the symmetric nuclear matter EoS are, however, plagued with
larger uncertainty. From inter-correlation of these higher order nuclear matter
parameters with lower order ones, we explore how they can be brought to more
harmonious bounds.
