Supernova explosions are among the most energetic events known in the universe, leaving supernova remnants (SNRs) as their relics. The cores of massive stars collapse to form neutron stars, among the most compact and strongest magnets in the cosmos. The thesis studies a sample of such magnetic "beauties" in X-rays, the magnetars and high-magnetic field pulsars (HBPs), with the motivation to understand their evolutionary links. We also address the connection between these sources by investigating their environs through their securely associated SNRs. Magnetars have ultra-high magnetic fields B ~ 10^{14} - 10^{15} Gauss (G) and include the soft-gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs). The HBPs have magnetic fields B ~ 10^{13} - 10^{14} G, intermediate between the classical rotation-powered pulsars (B ~ 10^{12} G) and magnetars.

We focussed on two HBPs: J1119-6127 and J1846-0258, with similar spin-properties and associated with the SNRs G292.2-0.5 and Kes 75, respectively. In our studies, magnetar-like behavior was discovered from the Crab-like pulsar J1846-0258, clearly establishing a connection between the HBPs and magnetars for the first time, while no such behavior has been observed from PSR J1119-6127 so far. J1119-6127's overall X-ray properties together with its compact pulsar wind nebula resemble more the classical rotation-powered pulsars. We studied two magnetars, one from each sub-class: SGR 0501+4516 and AXP 1E 1841-045. The spectral and statistical analysis of the bursts and the persistent X-ray emission properties observed from them were found consistent with the magnetar model predictions as well as those seen in other SGRs. Finally, we probed the environment of these stellar magnets by performing a detailed X-ray imaging and spatially resolved spectroscopic study of two SNRs: G292.2-0.5 and Kes 73 associated with J1119-6127 and 1E 1841-045, respectively. We found that both SNRs point to very massive progenitors (>~25 solar masses), further supporting the growing evidence for magnetars originating from massive progenitors using other multiwavelength studies.