Intestacy refers to the state of dying without a valid will, so when someone dies without a will they have "died intestate." The opposite of dying intestate is dying testate. When there is no will, the people who receive your property and assets will be determined according to your state's intestacy law.
A surviving spouse and children, if you have them, almost always inherit your property when you die intestate, but otherwise your heirs under intestate succession law may not be who you wanted them to be — that’s why it’s imperative to make an estate plan that includes a last will and testament to make sure the people you want to receive your assets actually do.
Who inherits during intestacy when there is no will?
When someone dies without a will, the first question many people have is who inherits the estate. The answer is that when you die intestate, your heirs depends on who survives you and what the state dictates in their intestacy laws.
A surviving spouse will most likely inherit at least some of your assets, but they are not always entitled to everything. Direct descendants, like children or grandchildren may also be entitled to their own share of the inheritance, so the estate may be divided between them and the spouse.
Under intestacy laws, an adopted child is treated the same as a biological child, but stepchildren usually only inherit if the decedent (the deceased) legally adopted them. A registered domestic partner may not be granted the same inheritance rights as a spouse depending on the state, so they may not inherit anything unless they are included as beneficiary in the decedent’s will. You can ask an estate attorney for more information on local inheritance laws concerning domestic and civil partners.
Read more about what happens when you die without a will in different life scenarios.
Surviving spouse’s share of an intestate estate
Each state determines how much a spouse receives when someone dies in intestate. For example, under New Jersey intestacy law, when the decedent is survived only by a spouse and their children, the spouse gets everything. But the decedent’s parents will also inherit along with a surviving spouse if they are the only people left behind by the decedent. 
By contrast, New York intestacy law only specifies that: 
A surviving spouse would receive everything if there are no children
A surviving spouse receives $50,000 of the estate, plus half of the remaining estate if there are children.
If you live in a community property state, there may be additional laws about who inherits marital property, which is owned equally by both spouses. For example, when someone dies intestate in California, the surviving spouse inherits the decedent's share of community property, but under Texas intestacy law community property passes to the surviving spouse and children.
Check out this guide to wills and probate by state to see how intestacy law works where you live.
What is intestate succession?
Intestate succession is the order in which people inherit a deceased person’s property and assets when there is no will. It is determined by state law, which organizes the decedent's next of kin into different tiers or classes to determine who has a greater claim to an inheritance. Generally, surviving descendants that are more closely related to the deceased (like grandchildren), have a greater claim to the intestate property than more distant relatives (like second-cousins).
Here is a common example of intestate succession, in relation to the decedent:
Children, their lineal descendants (grandchildren, great-grandchildren, etc.)
Descendants of the decedent's parents, like siblings, nieces, and nephews
Grandparents, or their lineal descendants, like aunts, uncles, and cousins
How it works is that when someone does not leave behind a spouse, then their children inherit the estate. If there are no surviving children, then the decedent's parents would inherit. If there is no surviving parent, then siblings would inherit. If there are no siblings, then the sibling’s children (nieces and nephews) would inherit. If there are no nieces and nephews, then grandparents would inherit. If there are no grandparents, then the grandparents’ descendants — aunts and uncles would — would inherit, and so on down the line.
When someone dies intestate without any blood relatives, then in most cases their assets become property of the state (“escheats” to the state). Some state laws, however, may have provisions that allow your deceased spouse’s next of kin to inherit if there are no blood relatives left on your side.
Related article: What to do with an inheritance
Intestacy and probate
Probate is the process of administering an estate and settling the decedent’s affairs. If you die without a will, the collection of all of your property and belongings is known as the "intestate estate."
To probate an intestate estate, someone must petition the court to act as personal representative or administrator in lieu of an executor named in a will. (Read more about an executor vs administrator and what their exact duties are.) The decedent's surviving spouse or adult children tend to have priority to open probate during intestacy, but a non-related person may also qualify if they get written consent from surviving family members.
Not all assets are subject to probate — certain assets pass directly to a named beneficiary and can do so outside of probate and independent of intestacy laws. Additionally, intestate estates can still avoid probate if state law allows for the use of a small estate affidavit, and the estate qualifies.
During the probate process for intestate estates, someone who thinks they may have a right to inherit can approach the court for a determination of heirship; there will be a hearing to officially determine and recognize the deceased's rightful heirs.
If you need to apply for probate for someone who died in intestate, read this guide on how to file for executor of estate without a will.
Why you should avoid dying intestate
Intestacy could lead to a lot of hurt feelings and arguments amongst those you leave behind. When you don’t name beneficiaries or create an estate plan, people will be left wondering what you truly would have wanted, and loved ones outside of your immediate family may not end up receiving the inheritance you intended for them.
Administering an intestate estate, depending on the size, can be a lengthy process — it might take years before an heir can receive a share of the inheritance from a large and complicated estate. The easiest way to avoid intestacy is to write a will that clearly stipulates your beneficiaries and assets. You can also avoid issues by naming contingent beneficiaries in case something happens to your primary beneficiaries.