The Convention came into force on 24 April 1972 but it is important to bear in mind that it was just an agreement and was not in itself a law. It was left up to individual nations to implement the Convention in their own laws upon ratifying or accepting it. Since laws are not usually retroactive, compliance with them typically dates from the year each of those laws was passed, not that of the Convention. A chronological list of the years that nations ratified or accepted the Convention is published on the UNESCO website.
Although many museums and other institutions have adopted the year 1970 as a cut-off point in the acquisition of antiquities, that year is purely voluntary - based on ethical rather than legal considerations. The Convention itself (Article 7a) advises that they should be prevented from acquiring cultural property which has been illegally exported after the date that both the country of origin and the country of the institution ratified or accepted the Convention. In the case of the UK acquiring an object from Turkey, for instance, that date would be 1 August 2002 (although Turkey ratified the Convention in 1981, it was not accepted by the UK until 21 years later). It is of course up to the institution to determine if an object is likely to contravene that rule and, as said, most set a much earlier date for ethical reasons.
A similar responsibility (and ethical awareness) is placed on dealers and collectors to ensure they do not acquire illicit cultural property (Article 5e). Although nations are exhorted to keep an up-to-date inventory of their national heritage (Article 5b), that cannot of course include individual objects as yet unknown in archaeological sites (Article 1c) and it is therefore incumbent on dealers and collectors to establish that an archaeological object was legally exported.
If a nation declares that its archaeological material is under threat of pillage, other signatories undertake to control international trade in the relevant material (Article 9). In the US, such measures are normally effected by means of a bilateral memorandum of understanding (MoU) under its implementation of the Convention (Convention on Cultural Property Implementation Act 1983). A summary of that Act is published by the US government.
The Convention also seeks to prohibit the import of cultural property stolen from a museum or similar institution or from a public monument (Article 7b), and return the property to its country of origin providing that it was documented and that compensation is paid where appropriate (the latter provision subject to certain conditions in the US). The UK stipulated that, in its own case, return was subject to its rules on limitation to claims (typically six years under the Limitation Act 1980).
As said, there appear to be common misconceptions about what the 1970 UNESCO Convention is and what it is not. This was recently highlighted by the comment submitted by an archaeologist to an online article regarding the questionable collecting habits of an elderly Australian digging up artefacts in the Middle East:
“The short answer is, yes, it was illegal [...] International law sets the deadline at 1970 — the date of the 1970 UNESCO Convention — for the removal of artifacts from the ground for collection. So if she began in 1967 and continued for 11 years (as the article states), then she was breaking the law.”The archaeologist was right to be outraged but, in fact, he was wrong about the 1970 UNESCO Convention. It is not "international law". Nor is there any "deadline at 1970". Australia did not accept it until 1989. Neither of course does the Convention have anything to do directly with "the removal of artifacts from the ground for collection". As its full title suggests, it concerns import, export and transactions.
The laws that the elderly Australian was probably breaking were those of the countries she was digging in. Her blatant disregard of those laws is reprehensible but it is important to employ the correct framework to condemn its illegality. In the case of Australia, the pertinent legislation is the Protection of Movable Cultural Heritage Act 1986, which sets no time limit for "unlawful imports".