The general rule of Islam is permissibility of all what is done by mankind; however certain undertakings are considered harmful for us and so they became prohibited. The most known are Riba (commonly translated with interest for money lent), Gharar (excessive uncertainty in contracts, e.g. regarding the object of a sale) and Maysir/Qimar (Gambling). Further Muslims shall not invest in certain prohibited activities such as alcohol, porc, pornography.
Aside from this core prohibitions, a typology of contracts is applied to vet, whether a certain financial transactions falls into the framework or outside of it.
Of course, there are also soft criteria like social responsiblity, being the trustee of Allah (God) on earth for mankind and environment.