These are a group of mainly multicellular, predominantly photosynthetic organisms.  Historically, any living thing not classified as animal was classified as a plant but now fungi and some algae have their own kingdoms.

There are many ways of classifying the plants but they can be classified using the standard system and this is used by various collections of biodiversity information and global species indexes like iNaturalist, Catalogue of Life, and NBA Atlas to name a few. The list below is taken from iNaturalist.

1. Phylum Anthocerotophyta — Hornworts
2. Phylum Bryophyta — Mosses
3. Phylum Charophyta — Charophyte Algae
4. Phylum Chlorophyta — Green Algae
5. Phylum Glaucophyta — Glaucophyte Algae
6. Phylum Marchantiophyta — Liverworts
7. Phylum Rhodophyta — Red Algae
8. Phylum Tracheophyta — Vascular Plants
   • Subphylum Angiospermae — Flowering Plants
     • Class Liliopsida — Monocots
     • Class Magnoliopsida — Dicots
   • Class Cycadopsida — Cycads
   • Class Ginkgoopsida — Ginkgos
   • Class Gnetopsida — Gnetophytes
   • Class Lycopodiopsida — Lycophytes
   • Class Pinopsida — Conifers
   • Class Polypodiopsida — Ferns

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I will use the system above. An overlapping system based on divisions is also used. My understanding of this is hazy at best but I have tried to give more details, as I have understood it, below.

The land plants can be subdivided into non-vascular and vascular plants. Vascular plants can be further subdivided into seedless and seed plants.

Non-vascular Plants (Bryophytes)

These lack specialised vascular tissue, xylem,  for support and water and food conduction, although some have cells forming a similarly functioning tissue called hydroids. They do not have true roots, stems or leaves. These are now divided into 3 divisions:

• Division Bryophyta (mosses)
• Division Marchantiophyta (liverworts)
• Division Anthocerotophyta (hornworts)

Vascular Plants (Tracheophytes)

These all contain xylem (support and water-conducting tissue) and phloem (food-conducting tissue) and therefore have true stems, leaves and roots.  They are often further subdivided into seeded and non-seeded plants.

Seedless Plants (Pteridophytes)

These are now all small herbaceous plants but the division used to be very diverse and included some large trees back in the Carboniferous period.  Ferns are not always classified at a division level but included here for now.

• Division Lycopodiophyta (aka Lycophyta):
  
  • Class Lycopodium (club mosses)
  • Class Selaginella (spike mosses)
  • Class Isoetes (quillworts)
• Division Pteridophyta:
  
  • Class Polypodiophyta or Polypodiopsida (ferns)
  • Class Psilotophyta or Psilotopsida (whisk ferns)
  • Class Sphenophyta or Equisetopsida (horsetails)
  • Class Marrattiopsida (giant ferns)

Seed Plants

These share many features with ferns but unlike ferns, the seed plants have stems that branch laterally and vascular tissue that is arranged in strands (bundles) around the pith (eustele). They also reproduce via seeds. These are often subdivided into gymnosperms (naked seed) and angiosperms.

Gymnosperms

These were the first plants to have seeds which are often referred to as naked seeds as they don’t have an outer covering around the seeds. They don’t have flowers or fruits and are wind-pollinated. They are among the largest and oldest living organisms. There are 4 divisions:

• Division Ginkgophyta (ginkgoes – only surviving species is Ginko biloba, the maidenhair tree)
• Division Cycadophyta (cycads)
• Division Gnetophyta (gnetophytes)
• Division Coniferophyta or Pinophyta (pines, yews, spruces, firs, junipers, redwoods, and others)

Angiosperms

There is just the one division

• Division Anthophyta or Magnoliophyta (flowering plants)

These reproduce using flowers and seed-containing fruits.  They have been classified in several different ways the earliest is referred to as the artificial classification system based on similar characteristics eg flower colour. Then came the Natural Classification system based on anatomical features, chemistry etc. The Angiosperm Phylogeny Group IV (APG IV) botanical system, is the most recent and incorporates DNA studies.  This includes them all at the division level with the division name Anthophyta with only informal groups recognised above the level of order.

Traditionally the flowering plants have been classified as dicotyledonous or monocotyledonous

• Monocots (grasses, rushes, sedges, cattails and pond weeds, palms, pineapple and other bromeliads, lilies, bananas, ginger, orchids, and others)
• Dicots or broad-leaved plants (most trees, buttercups, poppies, roses, violets, cacti, mints, squashes, sunflowers, and many others).

More recently the 8 groups of living angiosperms have been separated as follows

• Basal angiosperms (ANA: Amborella, Nymphaeales, Austrobaileyales)
  • Amborella (a single species of shrub from New Caledonia)
  • Nymphaeales (about 80 species, water lilies and Hydatellacea)
  • Austrobaileyales (about 100 species of woody plants from various parts of the world)
• Core angiosperms (Mesangiospermae)
  • Chloranthales (77 known species of aromatic plants with toothed leaves)
  • Magnoliids (about 9,000 species, characterised by trimerous flowers, pollen with one pore, and usually branching-veined leaves — eg. magnolias, bay laurel, and black pepper)
  • Monocots (about 70,000 species, characterised by trimerous flowers, a single cotyledon, pollen with one pore, and usually parallel-veined leaves — eg. grasses, orchids, and palms)
  • Ceratophyllum (about 6 species of aquatic plants, perhaps most familiar as aquarium plants)
  • Eudicots (about 175,000 species, characterised by 4- or 5-merous flowers, pollen with three pores, and usually branching-veined leaves — eg. sunflowers, petunia, buttercup, apples, and oaks)

The relationships between many of these are still unclear so I expect there will be further changes.  Where I have photos I will list them from the level of order.