Pteridophytes are vascular plants with differentiated roots, stems, and leaves that reproduce sexually via oogamy. They primarily exist as sporophytes that produce spores in sporangia, and are classified into four divisions: Psilophyta, Lycopodophyta, Equisetophyta, and Filicophyta, each with distinct characteristics. The sporophyte lifecycle involves haploid gametophytes which form male and female reproductive organs, with fertilization requiring water.