In sentences like "I am looking forward to receiving your reply", "to" is being used as a preposition rather than to form an infinitive. I know it's confusing, but you should look at "to receiving" as two separate grammatical units – a gerund followed by a preposition. In sentences like "I want to receive your reply", you should think of "to receive" as a single grammatical unit. Does this make sense? Embarrassingly, I am not 100% sure of my answer despite being a native English speaker. Usage of -ing forms in English is very unpredictable and I rarely think about why I use gerunds. I am curious to hear what other native English speakers think.

As the previous answer touched upon, "ing" words are often "gerunds"- this means they function as nouns. For example- "I like running." In your sentence, "receiving" is a gerund and as a noun can be placed after prepositions. Here are a few more examples of gerunds: We don't think waiting is a bad idea. Cooking is easy once you learn some recipes. He changed his focus to learning grammar.

As, for example, I am used to cooking on sundays? I am accostumed to cooking on sundays? http://www.englishteachermelanie.com/grammar-can-a-gerund-be-used-after-to/