In a nutshell

Dose:         A concentration of a chemical that might evoke a reaction in living organisms
Response: Biological reaction to a given dose (also called: endpoint or outcome or y)

Responses: Continuous, Counts, Binary

Use of Self starter function (no guesstimates any more)
Fitting function drm()
One of more curves fitted separately or simultaneously
Parameter constraint possible

After fitting functions

EDx effective dose
Relative potency at any one EDx
Comparison of parameters

The most recent published paper on the drc package is from 2015: Dose-Response Analysis Using R
From Abstract
Dose-response analysis can be carried out using multi-purpose commercial statistical software, but except for a few special cases the analysis easily becomes cumbersome as relevant, non-standard output requires manual programming. The extension package drc for the statistical environment R provides a flexible and versatile infrastructure for dose-response analyses in general…. The aim of the present paper is to provide an overview of state-of-the-art dose-response analysis, both in terms of general concepts evolved and matured over years and by means of concrete examples.

The first paper was published in 2005: Bioassay Analysis Using R

If you want to know more and use the facilities of  drc  go to the dose-response chapter:
STATISTICAL ANALYSIS OF AGRICULTURAL EXPERIMENTS WITH R