What does filiation mean?
Filiation has been defined as the civil status of a child in relation to his or her father or mother.
What are the kinds of filiation of children?
Under Article 163 of the Family Code, the filiation of children may be by nature or by adoption. Further, natural filiation may be legitimate or illegitimate.
Who are legitimate and illegitimate children? 
Legitimate children are those conceived or born during the marriage of the parents as provided for in Art. 164. Under the same provision of law, children conceived as a result of artificial insemination of the wife with the sperm of the husband or that of a donor or both are likewise legitimate children of the husband and his wife, provided that both of them authorized or ratified such insemination in a written instrument executed and signed by them before the birth of the child.
On the other hand, children conceived and born outside a valid marriage are illegitimate under Art. 165.
What are the rights of legitimate and illegitimate children? 
A. Legitimate children
Art. 174 provides that legitimate children shall have the right:
(1) to bear the surnames of the father and the mother;
(2) to receive support from their parents, their ascendants, and in proper cases, their brothers and sisters; and
(3) to be entitled to the legitime and other successional rights granted to them by the Civil Code.
B. Illegitimate children
Art. 176 provides for the rights of illegitimate children, to wit:
(1) use the surname of the mother;
(2) be under the parental authority of their mother;
(3) be entitled to support; and
(4) be entitled to one-half of the legitime of a legitimate child.
With regard to (1) above, the same provision of law provides for an exception when illegitimate children may use the surname of their father – if their filiation has been expressly recognized by their father through the record of birth appearing in the civil register, or when an admission in a public document or private handwritten instrument is made by the father. This is by virtue of Republic Act No. 9225, an act allowing illegitimate children to use the surname of their father, which amended Art. 176 of the Family Code.
Is there a way for an illegitimate child to become legitimate without the process of adoption?
Yes, an illegitimate child may become legitimate by way of legitimation.
Under Art. 177, a child may be legitimated if conceived and born outside of wedlock of parents who, at the time of conception of the former,
(a) were not disqualified by any impediment to marry each other; or
(b) were so disqualified only because either or both of them were below 18 years of age.
Once legitimated, they shall enjoy the same rights as legitimate children pursuant to Art. 179.
How does legitimation take place?
Legitimate shall take place by a subsequent valid marriage between parents.
Under the rules implementing R.A. No. 9858, legitimation is initiated through an Affidavit of Legitimation which shall be registered with the Local Civil Registrar's Office where the child was born.
 This classification is based on Title VI – Paternity and Filiation of the Family Code. There are several other provisions of the law which provides for specific instances when a child is considered legitimate or illegitimate, such as Art. 54.
 The enumeration is based on Title VI – Paternity and Filiation of the Family Code. Other provisions of law may provide for other rights of legitimate and illegitimate children.
 As amended by R.A. No. 9858, an act providing for the legitimation of children born to parents below marrying age.
 Art. 178, Family Code.