When all of this goes into effect, and when you'll notice the changes
To be clear, unless I've noted otherwise, the changes made by the tax reform bill go into effect for the 2018 tax year, which means you'll first notice them on your tax return that you file in 2019.
However, you can expect to see a change in your paychecks after Jan. 1, as employers will modify their withholdings to adapt to the newly passed 2018 tax brackets

Most of the individual tax breaks are temporary
So far, we've discussed the tax changes that will affect individuals. It's also important to point out that most of the changes to individual taxes made by the bill are temporary -- they're set to expire after the 2025 tax year.

The notable exception is the change to the Chained CPI as a means to calculate inflation. In simple terms, this means that the income thresholds for each marginal tax bracket will rise more slowly than they previously would, which will presumably make a greater portion of each worker's income subject to higher marginal tax rates over time.

The combination of the temporary nature of the tax cuts and the permanent switch to the Chained CPI is expected to have the eventual effect of higher taxes on the middle class, as compared to current tax law.

A different way to calculate inflation
Perhaps one of the most significant, but least talked-about, provisions in the new tax bill is the switch in the way inflation is calculated.

Under the previous tax law, inflation is measured by the consumer price index for all urban consumers, also known as the CPI-U, which essentially tracks the cost of goods and services that affect the typical household.

The new law adopts a metric called the Chained CPI. Essentially the key difference is that the Chained CPI assumes that if a particular good or service gets too expensive, consumers will trade down to a cheaper alternative.

The effect is that the Chained CPI grows slower than the traditionally used CPI-U. This means that tax bracket thresholds will rise slower, as will other IRS inflation-sensitive numbers, such as eligibility limits for certain deductions and credits.

The estate tax exemption

The estate tax already applied to a small percentage of households. Essentially, the 40% estate tax rate applied only to the portion of an estate that was valued at $5.6 million or more per individual, or $11.2 million per married couple.
However, the new tax law exempts even more households by doubling these exemptions. Now, for 2018, individuals get a $11.2 million lifetime exemption and married couples get to exclude $22.4 million. As you can probably imagine, this won't leave too many families paying theĀ estate tax.