Under US tax laws US Citizens ; Green Card Holders , H1 visaholder residing in USA or abroad ; an individual who has stayed in USA for 183 days or more and  a US Tax Resident is required to declare overseas income and financial assets . Brief details and penalties for failure are mentioned herein :

1.    GLOBAL INCOME TAXED IN USA and  worldwide income is to be reported in US tax return subject to tax credit for taxes paid abroad .
.02  Penalty for failure attracts additional taxes , interest , fines & in extreme cases even imprisonment. 
.03 IRS weblink : https://www.irs.gov/individuals/international-taxpayers/taxpayers-living-abroad

2.    FILE REPORT OF FOREIGN BANK AND FINANCIAL ACCOUNTS (FBAR) if overseas institutional financial accounts wherein one has signing authority exceeds US$ 10,000 any time during the year.
.02    Penalty for failiure to report is $10,000 per violation. However penalty for willful violation is minimum $ 100,000 or 50% of account balance, whichever is higher.
.03 IRS weblink :http://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Report-of-Foreign-Bank-and-Financial-Accounts-FBAR

3.   FILE REPORT OF FOREIGN ACCOUNT TAX COMPLIANCE ACT (FATCA) if all financial accounts including Personal Loans, Partnership Investments, etc. exceed US$ 100,000 as on 31st December or US $ 150,000 during the year in case of marrried joint returns in Form 8938 alongwith Form 1040 . 
02    Failure to file Form 8938 by due date or filing an incomplete form attracts penalty of $10,000.
.03 IRS weblink : https://www.irs.gov/businesses/corporations/summary-of-fatca-reporting-for-us-taxpayers

4.   GIFT RECEIVED REQUIRES REPORTING in Form 3520 if the amount of gift received exceeds US$ 100,000.
.02    Failure is subject to penalty up to 5% of the amount of the foreign gift for each month for which failure continues and can raise up to 35% if unreported gifts are received from Overseas Trust upon distribution.
.03  IRS weblink : http://www.irs.gov/instructions/i3520/

5.    INHERITANCE RECEIVED REQUIRES REPORTING in Form 3520 if the amount of inherited assets exceeds US$ 100,000.
.02    Failure is subject to penalty up to 5% of the amount of the foreign gift for each month for which failure continues and can raise up to 35% if unreported inherited assets received from Overseas Trust upon distribution.
.03  IRS weblink : http://www.irs.gov/instructions/i3520/ 

6.   GIFT GIVEN REQUIRES REPORTING in Form 709 if gift to each donee exceeds US$ 14000.  Lifetime gift and estate exclusion is  $5,340,000 for year 2014.
.02    Penalty for Non Payment of gift tax can range from 5% to 25% of the amount of gift.
.03  IRS weblink : www.irs.gov/pub/irs-pdf/i709.pdf 

7.   PASSIVE FOREIGN INVESTMENT COMPANY (PFIC) rules apply to gain of Overseas Mutual Funds.
.02   PFIC rules require computation and payment of tax on notional income i.e. Net Asset Value (NAV) as at the end of the year.
.03 IRS weblink : http://www.irs.gov/instructions/i8621/ch01.html

8.  IRS has also specified other Forms such as Form  5471 for reporting of investments in Foreign Corporation (Investment by each individual more than 10%) &  Form 8865 for investments in Foreign Partnership Firm (Investment by each individual more than 10%) etc.
.02  Failure attracts various penalties.

II.   IMMUNITY FROM FAILURE TO COMPLY ANY OF THESE CAN BE AVAILED UNDER SDOP (Streamlined Domestic Offshore Procedures) if the non compliance was on account of negligence subject to penalty of 5% of maximum value of last 6 yearends overseas financial assets ; revision of 3 years Fed tax returns  ; filing of 3 years FATCA returns ; filing of 6 years FBAR returns and Declaration stating reasons for failure.