We demonstrate that after more than six decades, estimates of global species richness have failed to converge, remain highly uncertain, and in many cases, are logically inconsistent."

Source : Global species richness estimates have not converged for Trends in Ecology & Evolution.

The paper cited above looked at the estimates for total land and marine animal species - which varied from 0.5 million to 10 million species.

A 2015 paper in the journal Proceedings of the National Academy of Sciences (using mathematical scaling-law methods to predict likely microbial species numbers) found that :

Using this scaling law combined with the lognormal model of biodiversity, we predict that Earth is home to as many as 1 trillion (10¹²) microbial species."

See Scaling laws predict global microbial diversity PNAS 113 (21) 5970-5975;

Current estimates are that, at best, only a tiny fraction of species on Earth have so far been properly catalogued and described.

A set of 2017 experiments at Stanford University, US, found that "Nearly all microbes inside us unknown to science"

Also see Definition of speciesplugin-autotooltip__plain plugin-autotooltip_bigDefinition of species

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"The species problem is the set of questions that arises when biologists attempt to define what a species is. Such a definition is called a species concept; there are at least 26 recognized species concepts. A species concept that works well for sexually reproducing organisms such as birds may be useless for species that reproduce asexually, such as bacteria."

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