As Camilo mentioned in the comments, “carbon neutral” in this context means zero net carbon emissions. This is the gross anthropogenic carbon emissions (fossil fuel burning and land use change) minus the carbon absorbed through managed practices. That distinction is important; you don’t include the carbon absorbed by the ocean and land through natural processes to offset gross emissions in the calculation.
Since 2010, the UN Environment Programme has published an “Emissions Gap” report each year that includes some relevant emissions numbers:
In 2017 greenhouse gas (GHG) emissions - excluding emissions from land-use change - reached a record 49.2 GtCO2e... Emissions from land-use change... added another 4.2 GtCO2, bringing the total to 53.5 GtCO2e.
Source: UNEP Emissions Gap Report 2018
The following is a nice schematic of various negative emission technologies (NETs) that could be used as mitigation in the overall budget:
Source: Smith et al (2016) “Biophysical and economic limits to negative CO2 emissions”, https://www.nature.com/articles/nclimate2870
Carbon capture and storage (CCS) is done at the point of burning fossil fuels, so reduces gross fossil emissions. Panel (g) is called LULUCF (Land Use, Land Use Change and Forestry) in the Emissions Gap reports and AFOLU (Agriculture, Forestry and Other Land Use) in the IPCC 1.5 Special Report, and that is effectively the +4.2 GtCO2e/year quoted above. The idea is that in the future land management will have to change to turn managed land from a net source to a net sink of GHGs. As for Bio-energy Carbon Capture Systems (BECCS), the current levels are about zero, although there are a dozen or so demonstrator projects totalling about 0.001 GtCO2/year. So at the moment it barely makes a dent in the overall budget, but mitigation scenarios require it rising to an order of 10 GtCO2/year by 2050:
The energy production from the use of BECCS over time in a range of mitigation scenarios.
Source: van Vuuren et al (2018) “Alternative pathways to the 1.5 °C target reduce the need for negative emission technologies”, https://www.nature.com/articles/s41558-018-0119-8
The IPCC special report also has a nice schematic of how NETs contribute to emissions scenarios. Although there's no timescale on the schematic, most of the actual scenarios don't show any notable BECCS until 2030.
Figure 2.5 | Evolution and break down of global anthropogenic CO2 emissions until 2100
Source: Rogelj et al (2018) "Mitigation Pathways Compatible with 1.5°C in the Context of Sustainable Development", Chapter 2 of the IPCC Special Report on Global Warming of 1.5°C.