Alternative minimum tax, version 2.0
The alternative minimum tax, or AMT, was implemented to ensure that high-income Americans paid their fair share of taxes, regardless of how many deductions they could claim. Essentially, higher-income households need to calculate their taxes twice -- once under the standard tax 
system and once under the AMT -- and pay whichever is higher.
The problem is that the AMT exemptions weren't initially indexed for inflation, so over time, the AMT started to apply to more and more people, including the middle class, which it was never intended to affect.
So, the tax reform bill permanently adjusts the AMT exemption amounts for inflation in order to address this problem, and makes them significantly higher initially in 2018. Here's how the AMT exemptions are changing for 2018.
                                                                                2017                                       2018                                 
Tax Filing Status                               AMT Exemption Amount            AMT Exemption Amount
Single or Head of Household                    $54,300                                           
Married Filing Jointly                                  $84,500                                           
Married Filing Separately                           $42,250                                            

In addition, the income thresholds at which the exemption amounts begin to phase out are dramatically increased. Currently, these are set at $160,900 for joint filers and $120,700 for individuals, but the new law raises these to $1 million and $500,000, respectively.