Animal testing relates to the use of animals in experiments and development projects usually to determine toxicity, dosing and/or efficacy of the test chemical or product. In a product safety framework, data derived from animal testing is used to help determine the limits for safe use of chemicals in order to protect human and animal health, and the environment.
Whilst animal testing has in the past been considered a reliable means of assessing the risks of a substance or what most would call an ‘Ingredient’ of a product. Alternative non-animal tests are being developed and have been validated for a range of health effects. 
Personal care and laundry products sold in Australia are (generally) not tested on animals because there is just no need for it, the technology and raw material history is well established.
Australia’s regulatory framework for cosmetic ingredients, administered by NICNAS (National Industrial Chemicals Notification and Assessment Scheme), does not require any cosmetic product to be tested on animals and requires animal test data only in certain circumstances (and where there are no non-animal alternative tests available) if a company is introducing a new chemical ingredient into Australia.
The Australian government committed to introduce a ban on cosmetic testing on animals in 2016, which will be implemented in July 2018. Based on historical data it is estimated that the ban will prohibit the use of animal testing for more than 99% of the cosmetics introduced into Australia. The remaining less than 1% are circumstances where these chemicals are also used in other industries and this information is critical to ensure we protect consumers, the public and the environment.  The new law seeks to create a disincentive to use animals for unnecessary purposes by encouraging the use of alternative test methods.
The only situation where a company must test on animals is when the product is being exported to China. Chinese regulations require all personal care products sold in China to be tested on animals. The EU, India, Israel and NZ all have bans on testing cosmetics and ingredients on animals. India and Israel have import bans on cosmetic products and ingredients tested on animals. 
For information on whether a company tests on animals, check the parent companies ethics policy.
Internationally, companies that produce raw materials for products have in the past, and in some cases still do test their raw materials on animals, depending on the raw material. All raw materials have been tested on animals at one point or another. Eg. The LD50 test, which is listed on MSDS’s, is the median lethal dose. The value of LD50 for a substance is the dose required to kill half the members of a tested population after a specified test duration, it is used as a general indicator of a substances acute toxicity. . In many cases it is unnecessary to test again, since the physically and chemical properties of the raw material are the same, and this can be tested analytically.
Animal testing is permitted to meet EU obligations for substances that are used for multiple purposes i.e. not solely in cosmetics, this includes detergents, but this can only be used as a last resort.
In line with ICH (International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use) guidelines and the REACH (Registration, Evaluation, Authorisation and Resitriction of Chemicals in the EU) regulation, research-based chemical and pharmaceutical companies are statutorily required to perform animal tests when developing new drugs in order to test the product safety of biological preparations and chemicals. International laws require animal research to be performed prior to testing the effect of new drugs in humans, or prior to marketing chemicals on a large scale.
Animal research is only permitted if there are no recognized alternative methods available, otherwise the alternative methods must be utilized. Animal research is, however, still unavoidable in many fields and frequently cannot be replaced by alternative testing.
There are improvements in the development of skin tissue models , and companies, such as Unilever  are currently working with the Chinese government to encourage adopting new technology and methodology, such as tests validated by the Organisation for Economic Co-operation and Development (OECD), computer based modelling and information from existing animal test data of a similar chemical, in order to avoid testing on animals.
It should be noted that this is an emerging area of research with some non-animal test methods not yet available for all health effects, either because they have not yet been developed or because they are still in the process of evaluation and validation. 
 Ban on the testing of cosmetics on animals Background paper, Australian Government Department of Health
 The Parliament of the Commonwealth of Australia House of Representatives, Industrial Chemicals Bill 2017, Explanatory Memorandum