The new tax law and what you need to know from the prospective of an Estate and Business Planning Attorney:

The below changes are generally effective January 1, 2018. The provisions relating to individual taxpayers all sunset after December 31, 2025, with the law reverting to prior law.

Estate & Gift Tax-related provisions:

The Estate and gift tax exemption is doubled. The basic exclusion amount increases from $5 million to $10 million, adjusted for inflation after 2011. In 2018, the exclusion will be $11.2 million per person. With a properly drafted trust, a couple could pass $22.4 million free from tax.
The Generation-Skipping Transfer tax exemption is still tied to the Estate and Gift tax exemption. So, it too doubles from $5 million to $10 million with inflation adjustment after 2011. The GST exemption will be $11.2 million in 2018.

Individual Income Tax Provisions:

Same number of brackets, but some rates are lowering.

Here are the new brackets:

10% (income up to $9,525 for individuals; up to $19,050 for married couples filing jointly)
12% (over $9,525 to $38,700; over $19,050 to $77,400 for couples)
22% (over $38,700 to $82,500; over $77,400 to $165,000 for couples)
24% (over $82,500 to $157,500; over $165,000 to $315,000 for couples)
32% (over $157,500 to $200,000; over $315,000 to $400,000 for couples)
35% (over $200,000 to $500,000; over $400,000 to $600,000 for couples)
37% (over $500,000; over $600,000 for couples)

The personal exemption, which would have been $4,150 per person in 2018, is eliminated. However, the child tax credit doubles from $1,000 to $2,000. Further the credit phases out at $400,000 instead of $110,000 for joint filers under prior law.
Alternative minimum tax remains for individuals, but the exemption increases. (The AMT is eliminated for corporations.)
The standard deduction amount for 2018 increases from $6,500 to $12,000 for an individual and from $13,000 to $24,000 for a married couple filing a joint return.
State and local taxes had been deductible in full. Beginning in 2018, state and local taxes are only deductible up to $10,000 in aggregate. This includes income taxes and property taxes. The limit is the same for individuals and married couples filing jointly. The limit for a married person filing separately is $5,000.
Interest on a home mortgage for a first or second residence had been deductible up to $1 million in debt (adjusted from inflation). Under the new law, the mortgage must be no larger than $750,000 for the interest to be deductible.
The penalty for not having health insurance is removed.
Various amounts in the tax code are indexed for inflation. The method of indexing has been changed to chained-CPI, which will raise levels more slowly than in the past.
Income from pass-through entities, such as S corporations, partnerships, sole proprietorships, etc., may now qualify for a 20% deduction. However, there are limits and phase-outs. For example, if the income is from a service business, the deduction is phased out if the taxpayer’s income is over $157,500 (or double that if married filing jointly).

Corporate Taxes:

Corporate taxes are changing the most. The rate of taxation for a C corporation changes from 35% to 21%.
A business may elect to expense property under Section 179 rather than depreciating it over years. The amount of property which could be expensed had been $500,000. Now, the limit for expensing is doubled to $1 million.
An S Corp shareholder may be an Electing Small Business Trust. Under current law an ESBT beneficiary may not include a non-resident alien. Now it can.