1. Introduction

2. A sample of luminous compact galaxies
2.1. Selection criteria
2.2. A Luminosity Upper Limit
2.3. Blue compact dwarf, green pea and luminous compact galaxies: a continuum in luminosity
2.4. Low-metallicity AGNs in Green Pea Galaxies
2.5. The [O III] λ 5007/Hβ vs. [N II] λ 6583/Hα diagram

3. Element abundances

4. Luminosity-metallicity relation

5. Stellar masses
5.1. Method
5.2. Masses of young and old stellar populations

6. Younger starbursts are hotter and denser than older ones

7. Mass-metallicity relation

8. Star formation rate

9. Age of stellar populations and the burst mode of star formation in LCGs

10. Conclusions