Observing the supernovae (SNe) associated to the different types of gamma-ray bursts (GRBs) is one of the few means to study their progenitors. In the past years, it has become clear that GRB-like events are more heterogeneous than previously thought. There is a marked difference between long GRBs, which are produced by the collapse of very massive stars and are normally associated with broad-lined type Ic SNe, and short bursts, which occur when two compact objects merge and that, at least in some cases, can produce an associated kilonova. Moreover, the SNe associated with different sub-types of long GRBs are also seen to differ, especially those associated with ultra-long duration GRBs. To address this issue in a systematic way we started an observing programme in 2010 at the 10.4m GTC telescope. Here we present some results of our programme, including the detection of 12 new GRB-SNe. Highlights of our sample are the discovery of the first spectroscopic SN associated with a highly energetic (E_γ,iso ∼ 10⁵⁴ erg) "cosmological" burst (GRB 130427A), the study of the SN associated with a shock-breakout GRB (GRB 140606B) and the SN associated with the peculiar ultra-long GRB 101225A at z = 0.85. The sample includes also the follow-up of several short GRBs in search for kilonovae emission (GRB 130603B and GRB 160821B are important examples). Amongst our latest results we present the photometric and spectroscopic observations of the SNe associated with GRB 150818A and GRB 161219B.