Extragalactic giant H II regions (EGHRs) are sites of active, concentrated star formation on manageable scales, and thus provide ideal labs to analyze starburst phenomena. To get a complete picture of the starburst phenomenon, the critical characteristics we must investigate include star formation history and the interplay between massive stars and the interstellar matter. For starbursts in giant H II regions, a key issue is whether a tight cluster is formed and later becomes a globular cluster or distributed OB associations are formed and later disperse. In addition, the types of environments that can produce very luminous giant H II regions are not well understood. The high resolution and sensitivity of the Hubble Space Telescope (HST ) are ideal for detailed studies of EGHRs. We have searched the Hubble Legacy Archives (HLA) and found > 10 nearby galaxies within 20 Mpc, imaged in Hα and multi-band continuum. To determine the best methods for analyzing these data, we perform an in-depth analysis of the ten most luminous H II regions in M51, five of which are bonafide EGHRs with Hα luminosities > 10^39 ergs s^−1 . We use the Hα image to study the distribution and physical structure of the gas in each H II region and determine its Hα luminosity and required ionizing flux. We use the continuum images to determine whether massive, super star clusters (SSCs) are found in these H II regions, and use photometric measurements to determine the mass and age spread of the resolved stellar population. The stellar properties are then compared with the interstellar structures. The results help us lay the groundwork for studying EGHRs in multiple galaxies and elucidate the starburst phenomenon by investigating the role environment plays in the formation of EGHRs, the star formation history in an EGHR, and the evolution of EGHRs.In M51, the top 40 H II regions have Hα luminosities > 10^38 erg s^−1 , indicative of global, disk-wide star formation. Among the five bonafide EGHRs, four are powered by at least two clusters each with masses > 10^4 M. We find observational evidence in EGHRs of star formation that is triggered sequentially, via spiral density waves, and through the interaction of the dwarf galaxy NGC 5195, but require follow-up observations of ionized gas movements via optical spectroscopy for further confirmation. We port this analysis to nearby barred spiral galaxy M83 to perform an in-depth analysis of its top 3 H II regions ranked by Hα luminosity. We find less luminous H II regions than in M51 with correspondingly fewer massive powering clusters. The H II regions in M83 are also proportionally closer on average to the galactic center than the H II regions in M51. While the galactic bar in M83 may play a role in dissociating molecular clouds and clusters that are capable of producing EGHRs, the larger size of M51 and the interaction of M51 with NGC 5195 together likely spearhead the differences in bright H II regions between these galaxies; adding more H II regions from other HLA galaxies will help test this prediction.
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